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Super-connected arc-transitive digraphs

2009
*
Discrete Applied Mathematics
*

In this paper, we prove that a strongly

doi:10.1016/j.dam.2008.08.018
fatcat:szqnicoekre3tdq6yohagvpevm
*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. ...##
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A survey of line digraphs and generalizations

2021
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Discrete Mathematics Letters
*

In this paper we present a survey of line

doi:10.47443/dml.2021.s109
fatcat:xm2dyoqtw5hpxdzmwogtsjebn4
*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*. ...##
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V-SUPER VERTEX OUT-MAGIC TOTAL LABELINGS OF DIGRAPHS

2017
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Communications of the Korean Mathematical Society
*

Let D be a directed graph with p vertices

doi:10.4134/ckms.c150189
fatcat:kc3gyksbyndrjlhzihtwaxbsfy
*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. ...##
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From Subkautz Digraphs to Cyclic Kautz Digraphs

2018
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Journal of Interconnection Networks (JOIN)
*

Using these parameters, we also prove that sK(d, )

doi:10.1142/s0219265918500068
fatcat:fcbszgxcxbeehp3xob43yb36ra
*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] . ...##
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The power of digraph products applied to labelings

2012
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Discrete Mathematics
*

We also prove that if G is a (

doi:10.1016/j.disc.2011.08.025
fatcat:omrki7nv5ba77efuw63ej2gowq
*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 ...##
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From subKautz digraphs to cyclic Kautz digraphs
[article]

2017
*
arXiv
*
pre-print

Using these parameters, we also prove that sK(d,ℓ)

arXiv:1709.01882v1
fatcat:6enqlma4rfabxn34mxmjvhre6i
*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*. ...##
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ENUMERATING SUPER EDGE-MAGIC LABELINGS FOR THE UNION OF NONISOMORPHIC GRAPHS

2011
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Bulletin of the Australian Mathematical Society
*

forest F ,

doi:10.1017/s0004972711002292
fatcat:vh4kdobccfcydkk4mrbwvdjlyy
*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 . ...##
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Vertex Antimagic Total Labeling of Digraphs

2015
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Kyungpook Mathematical Journal
*

We show the existence

doi:10.5666/kmj.2015.55.2.267
fatcat:dzsxicbhg5cfhgq6ifvsfrt26i
*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. ...##
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:{unav)

2012
*
Annals of Operations Research
*

The objective is to maximize the benefit derived from making specific

doi:10.1023/a:1018945415148
fatcat:kiryau6k5vhmxg67gut7i4yjvm
*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. ...##
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Maximally edge-connected and vertex-connected graphs and digraphs: A survey

2008
*
Discrete Mathematics
*

The graph or

doi:10.1016/j.disc.2007.06.035
fatcat:3wbcspxdr5ewxgcxnnbvsqmukq
*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*. ...##
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Directed hypergraphs and applications

1993
*
Discrete Applied Mathematics
*

Concepts such as

doi:10.1016/0166-218x(93)90045-p
fatcat:ofrqtmphfvcm3op57jsck6s3iq
*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. ...##
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The Jumping Knight and Other (Super) Edge-Magic Constructions

2013
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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

doi:10.1007/s00009-013-0360-3
fatcat:ohzeaot2frap7kaivjpqqzntxm
*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 ...##
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A Graph-Theoretical Approach for Comparison Between the Pair of Allied Ragas Bhupali and Deshkar of North Indian Classical Music
[chapter]

2018
*
Asset Analytics
*

Definitions of musical graph, musical walk, multi-musical graph, musical cycle

doi:10.1007/978-981-13-0872-7_12
fatcat:dscprlq6orgh5be6uptjwh7zgm
*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*...##
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Characterization of super-radial graphs

2014
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Discussiones Mathematicae Graph Theory
*

The minimum eccentricity is called the radius, r(G), of the graph

doi:10.7151/dmgt.1769
fatcat:qhf6nmuewnacrhrh2zhsjdyl4u
*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 ...##
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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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