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Edge-Transitivity of Cayley Graphs Generated by Transpositions
Discussiones Mathematicae Graph Theory, 2016 Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note,
Ganesan Ashwin
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ON A CLASS OF EDGE-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS [PDF]
Ural Mathematical Journal, 2021 The paper is devoted to the problem of classification of edge-transitive distance-regular antipodal covers of complete graphs. This extends the classification of those covers that are arc-transitive, which has been settled except for some tricky cases ...
Ludmila Yu. Tsiovkina
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Normal edge-transitive and $ frac{1}{2}$-arc-transitive Cayley graphs on non-abelian groups of order $2pq$ , $p > q$ are primes [PDF]
International Journal of Group Theory, 2016 Darafsheh and Assari in [Normal edge-transitive Cayley graphs onnon-abelian groups of order 4p, where p is a prime number,Sci. China Math. {bf 56} (1) (2013) 213$-$219.] classified the connected normal edge transitive and$frac{1}{2}-$arc-transitive ...
Ali Reza Ashrafi, Bijan Soleimani
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Elementary abelian covers of the Wreath graph W (3, 2) and the Foster graph F26A
AKCE International Journal of Graphs and Combinatorics, 2023 Arc-transitive and edge-transitive graphs are widely used in computer networks. Therefore, it is very useful to introduce and study the properties of these graphs.
Z. Chen +5 more
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On Semisymmetric Cubic Graphs of Order 20p2, p Prime
Discussiones Mathematicae Graph Theory, 2021 A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be an arbitrary prime. Folkman proved [Regular line-symmetric graphs, J. Combin. Theory 3 (1967) 215–232] that there is no semisymmetric graph of
Shahsavaran Mohsen +1 more
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A Combinatorial Approach to the Computation of the Fractional Edge Dimension of Graphs
Mathematics, 2021 E. Yi recently introduced the fractional edge dimension of graphs. It has many applications in different areas of computer science such as in sensor networking, intelligent systems, optimization, and robot navigation.
Nosheen Goshi +3 more
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On transitivity and connectedness of Cayley graphs of gyrogroups
Heliyon, 2021 In this work, we explore edge direction, transitivity, and connectedness of Cayley graphs of gyrogroups. More specifically, we find conditions for a Cayley graph of a gyrogroup to be undirected, transitive, and connected.
Rasimate Maungchang +3 more
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Uniform edge betweenness centrality
Electronic Journal of Graph Theory and Applications, 2020 The edge betweenness centrality of an edge is loosely defined as the fraction of shortest paths between all pairs of vertices passing through that edge. In this paper, we investigate graphs where the edge betweenness centrality of edges is uniform. It is
Heather Newman +3 more
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The edge-regular complete maps
Open Mathematics, 2020 A map is called edge-regular if it is edge-transitive but not arc-transitive. In this paper, we show that a complete graph Kn{K}_{n} has an orientable edge-regular embedding if and only if n=pd>3n={p}^{d}\gt 3 with p an odd prime such that pd≡3{p}^{d ...
Yu Xue, Lou Ben Gong
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A Novel and Efficient Method for Computing the Resistance Distance
IEEE Access, 2021 The resistance distance is an intrinsic metric on graphs that have been extensively studied by many physicists and mathematicians. The resistance distance between two vertices of a simple connected graph $G$ is equal to the resistance between two ...
Muhammad Shoaib Sardar +3 more
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