Results 71 to 80 of about 420,658 (213)
Constructing Independent Spanning Trees on Pancake Networks
IEEE Access, 2020 For any graph G, the set of independent spanning trees (ISTs) is defined as the set of spanning trees in G. All ISTs have the same root, paths from the root to another vertex between distinct trees are vertex-disjoint and edge-disjoint.
Dun-Wei Cheng +2 more
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Complete Rotations in Cayley Graphs
European Journal of Combinatorics, 2001 Consider a Cayley graph \(\text{Cay}(G,S)\) of a finite group \(G\) generated by a set \(S=S^{-1}=\{s_0,\ldots,s_{|S|-1}\}\) where \(1\notin S\). A bijection \(\omega:G\to G\) is called a complete rotation of the graph if \(\omega(1)=1\) and \(\omega(xs_i)=\omega(x)s_{i+1}\) for all \(x\in G\) and all \(i\in{\mathbb{Z}}_{|S|}\).
Marie-Claude Heydemann +2 more
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Representations of Borel Cayley Graphs [PDF]
SIAM Journal on Discrete Mathematics, 1993 Summary: There is a continuing search for dense \((\delta, D)\) interconnection graphs, that is, regular, undirected, degree \(\delta\) graphs with diameter \(D\) and having a large number of nodes. Cayley graphs formed by Borel subgroups currently contribute to some of the densest known \((\delta =4,D)\) graphs for a range of \(D\). However, the group
K. Wendy Tang, Bruce W. Arden
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On a Ramsey–Turán variant of Roth's theorem
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract A classical theorem of Roth states that the maximum size of a solution‐free set of a homogeneous linear equation L$\mathcal {L}$ in Fp$\mathbb {F}_p$ is o(p)$o(p)$ if and only if the sum of the coefficients of L$\mathcal {L}$ is 0. In this paper, we prove a Ramsey–Turán variant of Roth's theorem, with respect to a natural notion of “structured”
Matija Bucić +4 more
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Pentavalent arc-transitive Cayley graphs on Frobenius groups with soluble vertex stabilizer
Open Mathematics, 2019 A Cayley graph Γ is said to be arc-transitive if its full automorphism group AutΓ is transitive on the arc set of Γ. In this paper we give a characterization of pentavalent arc-transitive Cayley graphs on a class of Frobenius groups with soluble vertex ...
Liu Hailin
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Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Isomorphisms of generalized Cayley graphs
Ars Mathematica Contemporanea, 2018 Summary: In this paper, we investigate the isomorphism problems of the generalized Cayley graphs, which are generalizations of the traditional Cayley graphs. We find that there are two types of natural isomorphisms for the generalized Cayley graphs. We also study the GCI-groups among the generalized Cayley graphs, and the Cayley regressions of some ...
Xu Yang, Weijun Liu, Lihua Feng
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Groups with a finite Busemann boundary are virtually cyclic
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric‐functional boundary. We show that if there exists a Cayley graph with finitely many Busemann points, then the underlying group is virtually cyclic.
Corentin Bodart +2 more
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Discrete Mathematics, 2001 The author considers the Cayley graphs \(\Gamma\) of a group \(G\) which have the property that \(\Aut\Gamma= L(G)R(G)\), where \(L(G)\) and \(R(G)\) denote the left and the right regular representation of \(G\). He proves that this equation holds if and only if \(\Gamma\) is a graphical regular representation of \(G\cong (\mathbb{Z})^n\) \((n> 4)\).
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Journal of Combinatorial Designs, Volume 34, Issue 7, Page 306-329, July 2026.ABSTRACT In this paper, we study and characterise the natural embedding of the twisted triality hexagon T ( q 3 , q ) in PG ( 7 , q 3 ). We begin by describing the possible intersections of subspaces of PG ( 7 , q 3 ) with T ( q 3 , q ). Then, we provide conditions on a set of lines ℒ, which ensure that ℒ forms the line set of a naturally embedded ...
Sebastian Petit, Geertrui Van de Voorde
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