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Some inequalities about connected domination number

Cheng Bo, Bolian Liu
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
In this note, 7c, ir, ~',i,/~0, F, IR denote the connected domination number, the irredundance number, the domination number, the independent domination number, the independence number, the upper domination  ...  We prove that 7c~<3ir-2 for a connected graph G. Thus, an open problem in discuss further some relations between 7c and 7, [~o,F. IR. respectively.  ...  We are grateful to the referee for many careful revisions and pointing out to us that some ideas in the proof of Theorem 2.4 are similar to those in [2] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(95)00088-e">doi:10.1016/0012-365x(95)00088-e</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cr2qhrcr3bamdeq6neqdwnv3su">fatcat:cr2qhrcr3bamdeq6neqdwnv3su</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171003060501/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/c5d/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDEyMzY1eDk1MDAwODhl.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b1/3a/b13a6c5c8a6cacfead37b3ba87c6d0871239d656.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(95)00088-e"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A note on dominating sets and average distance

Ermelinda DeLaViña, Ryan Pepper, Bill Waller
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
We show that the total domination number of a simple connected graph is greater than the average distance of the graph minus one-half, and that this inequality is best possible.  ...  In addition, we show that the domination number of the graph is greater than two-thirds of the average distance minus one-third, and that this inequality is best possible.  ...  Hence, every spanning tree of G is a trunk for G, and every connected dominating set is the vertex set of some trunk.  ... 
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A Study on Connected Domination Transition Number of a Graph

Kaspar S, B. Gayathri, D. Kalpanapriya, M. P. Kulandaivel3
<span title="2018-10-02">2018</span> <i title="Science Publishing Corporation"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/piy2nrvrjrfcfoz5nmre6zwa4i" style="color: black;">International Journal of Engineering &amp; Technology</a> </i> &nbsp;
Recently, some researchers attempted on transition of the domination parameter into a connected one.  ...  ., connected domination transition number was introduced and its properties and bounds were studied.  ...  Readers can refer to [6] to know more about the connected domination numbers transition number.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14419/ijet.v7i4.10.20916">doi:10.14419/ijet.v7i4.10.20916</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7bgxutft2vgkhpnogemd562sma">fatcat:7bgxutft2vgkhpnogemd562sma</a> </span>
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Networks in labor markets: Wage and employment dynamics and inequality

Antoni Calvó-Armengol, Matthew O. Jackson
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sj24t22gfnfprddmjorsfd6flq" style="color: black;">Journal of Economic Theory</a> </i> &nbsp;
We present a model of labor markets that accounts for the social network through which agents hear about jobs.  ...  if E [f ] E [f ] for every nondecreasing function f : R n → R. 15 The domination is strict if strict inequality holds for some nondecreasing f.  ...  Networks We say that i is connected to j if p i (w) = p i (w −j , w j ) for some w and w j .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jet.2005.07.007">doi:10.1016/j.jet.2005.07.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aiwormxqfbehjjiab7u3cvxlta">fatcat:aiwormxqfbehjjiab7u3cvxlta</a> </span>
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The number system hidden inside the Boolean satisfiability problem [article]

Keum-Bae Cho
<span title="2018-01-24">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In addition, I show that 2-SAT does not form the number system and Horn-SAT partially forms the number system according to the feasible value of the dominant variable.  ...  First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler.  ...  However, 2-SAT does not form the number system and Horn-SAT forms the number system only when the feasible value of the dominant variable is '0'. Proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.4426v3">arXiv:1406.4426v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3oaz3xp5azfafo2kluc5lwxn2u">fatcat:3oaz3xp5azfafo2kluc5lwxn2u</a> </span>
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Agent-Based Model Heuristics in Studying Memory Mechanisms

Alexandr A. Ezhov, Svetlana S. Terentyeva
<span title="">2014</span> <i title="Scientific Research Publishing, Inc,"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jxkgrvdwjfbf3iznpywuhrujsu" style="color: black;">Psychology</a> </i> &nbsp;
This study is aimed at proposing an agent-based model formulated in (Ezhov & Khrennikov, 2005) and describing the emergence of specific binary memory codes in the system characterized by high inequality  ...  If we describe the memory of the given agent using the {A, R} or {S, G} codes, we may evidently lose some information about the true history.  ...  More information about the model properties can be revealed not from equilibrium distributions, but from the study of fluctuations, i.e. temporal deviations of agent-in-cell numbers from their equilibrium  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/psych.2014.55048">doi:10.4236/psych.2014.55048</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/spym6oostzebbatejl74yepixm">fatcat:spym6oostzebbatejl74yepixm</a> </span>
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On the Undirected Rural Postman Problem: Tight Bounds Based on a New Formulation

Elena Fernández, Oscar Meza, Robert Garfinkel, Maruja Ortega
<span title="">2003</span> <i title="Institute for Operations Research and the Management Sciences (INFORMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/atonzevfefa2vdbi3do6ad2jda" style="color: black;">Operations Research</a> </i> &nbsp;
Computational results are encouraging, especially in terms of the relatively small number of added inequalities needed to get good lower bounds, and the fact that the vast majority of these have efficient  ...  Dominance Relations and Valid Inequalities An Overview A number of authors have established valid inequalities and dominance relations for RPP.  ...  Dominance Relations Some of the formulations of RPP introduced in the next section are partially based on dominance relations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1287/opre.51.2.281.12790">doi:10.1287/opre.51.2.281.12790</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hdy64zeqovfjpmmyxvj4lcsb2i">fatcat:hdy64zeqovfjpmmyxvj4lcsb2i</a> </span>
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Upper bounds on the k-forcing number of a graph [article]

David Amos, Yair Caro, Randy Davila, Ryan Pepper
<span title="2014-01-23">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These results resolve a problem posed by Meyer about regular bipartite circulant graphs. Finally, we present a relationship between the k-forcing number and the connected k-domination number.  ...  As a corollary, we find that the sum of the zero forcing number and connected domination number is at most the order for connected graphs.  ...  Some of the many other papers written about zero forcing number are: [9, 14, 15, 19, 20, 22, 23, 25] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1401.6206v1">arXiv:1401.6206v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qsxz5x7ntvdb7om2tfzetntyoq">fatcat:qsxz5x7ntvdb7om2tfzetntyoq</a> </span>
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Page 7343 of Mathematical Reviews Vol. , Issue 97M [page]

<span title="">1997</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The ar- ticle concludes with some connections to codes, and several open questions.  ...  As applications, we give some structural properties of (k + 1)K>-free graphs, construct all 2K>-free graphs, and count the number of labeled 2K>-free connected bipartite graphs.” 97m:05208 05C70 Miller  ... 
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Introduction to dominated edge chromatic number of a graph [article]

Mohammad R. Piri, Saeid Alikhani
<span title="2020-03-19">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by χ_dom^'(G).  ...  Finally, we consider the k-subdivision of G and study the dominated edge chromatic number of these kind of graphs.  ...  Motivated by dominated chromatic number of graphs, we consider the proper edge coloring of G and introduce the dominated edge chromatic number of G, χ ′ dom (G), obtain some properties of χ ′ dom (G) and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2003.10232v1">arXiv:2003.10232v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pl6nfh7smbbxrc3n5zrlmb2oey">fatcat:pl6nfh7smbbxrc3n5zrlmb2oey</a> </span>
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Comparing Graphs of Different Sizes

RUSSELL LYONS
<span title="2017-05-02">2017</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/domxx2wewzae3e2m2ziqaqbyhm" style="color: black;">Combinatorics, probability &amp; computing</a> </i> &nbsp;
Our methods involve inequalities for determinants, for traces of functions of operators, and for entropy.  ...  Using them, we prove several theorems for such pairs that compare the number of spanning trees, the return probabilities of random walks, and the number of independent sets, among other combinatorial quantities  ...  I am grateful to Oded Schramm for discussions at the start of this project and to Prasad Tetali for conversations about Section 5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s096354831700013x">doi:10.1017/s096354831700013x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cyxix2excjbcxhb2ijztv3mvlu">fatcat:cyxix2excjbcxhb2ijztv3mvlu</a> </span>
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New Authoritarianism - A Research Note

György Csepeli, Gergő Prazsák
<span title="">2011</span> <i title="Expert Projects"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q5fi7rs3pvhbbf2ximdc3qxngq" style="color: black;">Sociologie Româneasca = Romanian Sociology</a> </i> &nbsp;
Still the averages do not say anything about the existence of some cognitive patterns which determine the attitude towards social dominance measured by the whole of the scale.  ...  , they opted for number 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://doaj.org/article/8939a0cc88d24e5091b4691b784167d4">doaj:8939a0cc88d24e5091b4691b784167d4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n7jf3hk5x5ebrnrgau3zg6bxxy">fatcat:n7jf3hk5x5ebrnrgau3zg6bxxy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201126120024/https://arsociologie.ro/revistasociologieromaneasca/sr/article/download/2011_1_csepeli/388/" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/60/94603fe494861c0e78527821eec5bd653c04b483.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Game domination number

Noga Alon, József Balogh, Béla Bollobás, Tamás Szabó
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
We determine the game domination number for several classes of graphs and provide general inequalities relating it to other graph parameters.  ...  The game domination number of the graph G, denoted by g(G), is the domination number of the directed graph resulting from this game.  ...  Now, we turn to some sparser graphs that (as expected) have larger game domination numbers. They also show that the game domination number can be much larger than the domination number.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(00)00358-7">doi:10.1016/s0012-365x(00)00358-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b7ayobluunac5d77h7lpo4spbm">fatcat:b7ayobluunac5d77h7lpo4spbm</a> </span>
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Introduction to dominated edge chromatic number of a graph

Mohammad R. Piri, Saeid Alikhani
<span title="">2021</span> <i title="AGHU University of Science and Technology Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e4qfzcz34faobatrg7utwpziby" style="color: black;">Opuscula Mathematica</a> </i> &nbsp;
The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by \(\chi_{dom}^{\prime}(G)\).  ...  We obtain some properties of \(\chi_{dom}^{\prime}(G)\) and compute it for specific graphs.  ...  DOMINATED EDGE CHROMATIC NUMBER OF SOME OPERATIONS ON A GRAPH Fig. 7 . 7 The graph G in Theorem 3.1 Fig. 8 .. 3 . 83 The graph G in Theorem 3There is a connected graph G and a vertex v ∈ V (G) which  ... 
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Page 6169 of Mathematical Reviews Vol. , Issue 90K [page]

<span title="">1990</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Three inequalities between the domination number (the maximum number of vertices of a dominating set) and the chromatic number of a finite undirected graph are presented.  ...  Ruth Bari (Silver Spring, MD) 90k:05072 05C15 05C35 Gernert, Dieter Inequalities between the domination number and the chromatic number of a graph. Discrete Math. 76 (1989), no. 2, 151-153.  ... 
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