Results 61 to 70 of about 472 (183)
Sensitivity and Hamming Graphs
Journal of Graph Theory, Volume 112, Issue 3, Page 296-305, July 2026.ABSTRACT For any m ≥ 3 we show that the Hamming graph H ( n , m ) admits an imbalanced partition into m sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong m‐ary Sensitivity Conjecture of Asensio, García‐Marco, and Knauer.
Sara Asensio +3 more
wiley +1 more source
Discrete Applied Mathematics, 1997 Given a quasigroup \(Q\) with a right identity element and a right-associative generating subset \(S\), a quasi-Cayley graph \(\text{QC}(Q,S)\) is constructed in very much the same way as a Cayley graph is constructed from a given group and a symmetric generating set.
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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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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
doaj +1 more source
Maximum Induced Trees and Forests of Bounded Degree in Random Graphs
Random Structures &Algorithms, Volume 68, Issue 4, July 2026.ABSTRACT The asymptotic behavior of the maximum sizes of induced trees and forests has been studied extensively in the last few decades, though the overall picture is far from being complete. In this paper, we close several significant gaps: (1) We prove 2‐point concentration of the maximum sizes of an induced forest and an induced tree with maximum ...
Margarita Akhmejanova +2 more
wiley +1 more source
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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Perfect Codes in Cayley Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2018 This is the final version that will appear in SIAM J.
He Huang, Binzhou Xia, Sanming Zhou
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Proper 3‐realizability and second cohomology of groups on two generators of finite order
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Given an (infinite) finitely generated group G$G$, its first cohomology group H1(G;ZG)$H^1(G;{\mathbb {Z}}G)$ is free abelian and “counts” the number of ends of G$G$ which equals 1+rank(H1(G;ZG))$1 + rank (H^1(G;{\mathbb {Z}}G))$. The question whether or not for every finitely presented group G$G$ its second cohomology group H2(G;ZG)$H^2(G ...
Francisco F. Lasheras, R. Roy
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