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Super-connected arc-transitive digraphs

Jixiang Meng, Zhao Zhang
2009 Discrete Applied Mathematics  
In this paper, we prove that a strongly connected arc-transitive oriented graph is either reducible or super-connected.  ...  Furthermore, if this digraph is also an Abelian Cayley digraph, then it is super-connected.  ...  The second author's research is supported by NSFC (60603003), the Key Project of Chinese Ministry of Education (208161) and Scientific Research Program of the Higher Education Institution of XinJiang.  ... 
doi:10.1016/j.dam.2008.08.018 fatcat:szqnicoekre3tdq6yohagvpevm

A survey of line digraphs and generalizations

2021 Discrete Mathematics Letters  
In this paper we present a survey of line digraphs and their generalizations.  ...  Frank Harary was the first to generalize this concept to digraphs. Since then various other generalizations have been proposed and studied.  ...  A digraph and its friends.We turn to connectedness properties of total digraphs. Assume first that D is strongly connected.  ... 
doi:10.47443/dml.2021.s109 fatcat:xm2dyoqtw5hpxdzmwogtsjebn4


Guruvaiah Durga Devi, Morekondan Subhash Raja Durga, Gurusamy Thevar Marimuthu
2017 Communications of the Korean Mathematical Society  
Let D be a directed graph with p vertices and q arcs.  ...  A vertex out-magic total labeling is a bijection In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such  ...  If a digraph D is connected and D has a V -SVOMT labeling with magic constant k, then k ≥ 2p + 1. Proof. If a digraph D is connected, then q ≥ p − 1.  ... 
doi:10.4134/ckms.c150189 fatcat:kc3gyksbyndrjlhzihtwaxbsfy

From Subkautz Digraphs to Cyclic Kautz Digraphs

2018 Journal of Interconnection Networks (JOIN)  
Using these parameters, we also prove that sK(d, ) and CK(d, ) are maximally vertex-connected and super-edge-connected.  ...  Closely related with these, the cyclic Kautz digraphs CK(d, ) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed.  ...  Observe that, since CK(d, 3) is the line digraph of sK(d, 2), the respective mean distance satisfies the inequality δ < δ * , in concordance with the results by Fiol, Yebra, and Alegre [7] .  ... 
doi:10.1142/s0219265918500068 fatcat:fcbszgxcxbeehp3xob43yb36ra

The power of digraph products applied to labelings

R. Ichishima, S.C. López, F.A. Muntaner-Batle, M. Rius-Font
2012 Discrete Mathematics  
We also prove that if G is a (super) (a, d)-edge-antimagic total tripartite graph, then nG is (super) (a ′ , d)-edge-antimagic total, where n ≥ 3, and d = 0, 2 and n is odd, or d = 1.  ...  We prove that if a (p, q)-digraph with p ≤ q is harmonious and h : E(D) −→ S n is any function, then und(D ⊗ h S n ) is harmonious.  ...  The research conducted in this document by second and fourth author has been supported by the Spanish Research Council under project MTM2008-06620-C03-01 and by the Catalan Research Council under grant  ... 
doi:10.1016/j.disc.2011.08.025 fatcat:omrki7nv5ba77efuw63ej2gowq

From subKautz digraphs to cyclic Kautz digraphs [article]

C. Dalfó
2017 arXiv   pre-print
Using these parameters, we also prove that sK(d,ℓ) and CK(d,ℓ) are maximally vertex-connected and super-edge-connected.  ...  Closely related to these, the cyclic Kautz digraphs CK(d,ℓ) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed.  ...  Using these parameters, we also prove that sK(d, ℓ) and CK(d, ℓ) are maximally vertex-connected and super-edge-connected.  ... 
arXiv:1709.01882v1 fatcat:6enqlma4rfabxn34mxmjvhre6i


2011 Bulletin of the Australian Mathematical Society  
forest F , and we study the super edge-magicness of an odd union of non-necessarily isomorphic acyclic graphs.  ...  A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f : In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear  ...  Let D be an acyclic digraph that is strong super edge-magic with respect to some linear forest F . Let |E(D)| = q and |E(F )| = q F . We denote by c(F ) the number of connected components of F .  ... 
doi:10.1017/s0004972711002292 fatcat:vh4kdobccfcydkk4mrbwvdjlyy

Vertex Antimagic Total Labeling of Digraphs

2015 Kyungpook Mathematical Journal  
We show the existence and nonexistence of (a, d)-vertex antimagic total labeling for several class of digraphs, and show how to construct labelings for generalized de Bruijn digraphs.  ...  In this paper we investigate the properties of (a, d)-vertex antimagic total labeling of a digraph D = (V, A).  ...  The authors are thankful to the anonymous referee for his/her valuable suggestions to improve the quality and the readability of the article.  ... 
doi:10.5666/kmj.2015.55.2.267 fatcat:dzsxicbhg5cfhgq6ifvsfrt26i


Lloyd Clarke, Ellis Johnson, George Nemhauser, Zhongxi Zhu
2012 Annals of Operations Research  
The objective is to maximize the benefit derived from making specific connections.  ...  We solve the ARP by Lagrangian relaxation and subgradient optimization and present computational results on real data from a major airline.  ...  Acknowledgements This work was partially supported by AFORS and NSF grants DDM-9115768 and SES-9122674.  ... 
doi:10.1023/a:1018945415148 fatcat:kiryau6k5vhmxg67gut7i4yjvm

Maximally edge-connected and vertex-connected graphs and digraphs: A survey

Angelika Hellwig, Lutz Volkmann
2008 Discrete Mathematics  
The graph or digraph D is called maximally edgeconnected if (D) = (D) and maximally vertex-connected if (D) = (D).  ...  In this survey we mainly present sufficient conditions for graphs and digraphs to be maximally edge-connected as well as maximally vertex-connected.  ...  Super-edge-connectivity Bauer et al. [11] proposed the concept of super-edge-connectedness.  ... 
doi:10.1016/j.disc.2007.06.035 fatcat:3wbcspxdr5ewxgcxnnbvsqmukq

Directed hypergraphs and applications

Giorgio Gallo, Giustino Longo, Stefano Pallottino, Sang Nguyen
1993 Discrete Applied Mathematics  
Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented.  ...  Palottino and S.  ...  .X if y is B-connected (Fconnected, BF-connected, super-connected) to s in the hypergraph X' obtained from ti by addition of a new origin node s and an arc (s, x) for each x E S.  ... 
doi:10.1016/0166-218x(93)90045-p fatcat:ofrqtmphfvcm3op57jsck6s3iq

The Jumping Knight and Other (Super) Edge-Magic Constructions

S. C. López, F. A. Muntaner-Batle, M. Rius-Font
2013 Mediterranean Journal of Mathematics  
Furthermore, if the function f meets the extra condition that f (V (G)) = {i} p i=1 then f is called a super edge-magic labeling and G is called a super edge-magic graph.  ...  We also use super edge-magic labelings of digraphs together with a generalization of the Kronecker product in order to get edge-magic labelings of some families of graphs.  ...  The research conducted in this document by the first and third authors has been supported by the Spanish Research Council under project MTM2011-28800-C02-01 and by the Catalan Research Council under grant  ... 
doi:10.1007/s00009-013-0360-3 fatcat:ohzeaot2frap7kaivjpqqzntxm

A Graph-Theoretical Approach for Comparison Between the Pair of Allied Ragas Bhupali and Deshkar of North Indian Classical Music [chapter]

Nandini Sarma, Pranita Sarmah
2018 Asset Analytics  
Definitions of musical graph, musical walk, multi-musical graph, musical cycle and connectivity of musical graph are then used for explaining various digraphs of music theory.  ...  (a) Arohana-Avarohana , (b) Catch Phrase and (c) Alap .  ...  <S (ak) , then S (ai) is said to be strength of rank i. o) Connectivity of a Musical Graph: The connectivity of a musical graph M may be defined as the total number of arcs in the graph divided by total  ... 
doi:10.1007/978-981-13-0872-7_12 fatcat:dscprlq6orgh5be6uptjwh7zgm

Characterization of super-radial graphs

Kumarappan Kathiresan, G. Marimuthu, C. Parameswaran
2014 Discussiones Mathematicae Graph Theory  
The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R  ...  In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u.  ...  Characterization of Super-radial Graphs  ... 
doi:10.7151/dmgt.1769 fatcat:qhf6nmuewnacrhrh2zhsjdyl4u

Page 792 of Mathematical Reviews Vol. , Issue 90B [page]

1990 Mathematical Reviews  
Hillis [The connection machine, MIT Press, Cambridge MA, 1986] for use in the design of a connection machine super-computer.  ...  Let G(V) (\V| =n) be a digraph with no multiple arcs (loops are allowed).  ... 
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