Results 51 to 60 of about 452 (178)
An extension of the cogrowth formula to arbitrary subsets of the tree
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract What is the probability that a random walk in the free group ends in a proper power? Or in a primitive element? We present a formula that computes the exponential decay rate of the probability that a random walk on a regular tree ends in a given subset, in terms of the exponential decay rate of the analogous probability of the non‐backtracking
Doron Puder
wiley +1 more source
Coxeter's enumeration of Coxeter groups
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In a short paper that appeared in the Journal of the London Mathematical Society in 1934, H. S. M. Coxeter completed the classification of finite Coxeter groups. In this survey, we describe what Coxeter did in this paper and examine an assortment of topics that illustrate the broad and enduring influence of Coxeter's paper on developments in ...
Bernhard Mühlherr, Richard M. Weiss
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Combination theorems for Wise's power alternative
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups and recover known results from a unified perspective. For groups acting on trees, we introduce a dynamical condition that allows us to deduce the power alternative for the group from the power ...
Mark Hagen +2 more
wiley +1 more source
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
doaj +1 more source
Integral Cayley Graphs and Groups [PDF]
SIAM Journal on Discrete Mathematics, 2014 We solve two open problems regarding the classification of certain classes of Cayley graphs with integer eigenvalues. We first classify all finite groups that have a "non-trivial" Cayley graph with integer eigenvalues, thus solving a problem proposed by Abdollahi and Jazaeri.
Ahmady, Azhvan +2 more
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Topological Aspects of Quadratic Graphs and M‐Polynomials Utilizing Classes of Finite Quasigroups
Journal of Mathematics, Volume 2026, Issue 1, 2026.Material science, drug design and toxicology studies, which relate a molecule’s structure to its numerous properties and activities, are studied with the use of the topological index. Graphs with finite algebraic structure find extensive applications in fields such as mathematics, elliptic curve cryptography, physics, robotics and information theory ...
Mohammad Mazyad Hazzazi +5 more
wiley +1 more source
UNIT AND UNITARY CAYLEY GRAPHS FOR THE RING OF EISENSTEIN INTEGERS MODULO \(n\)
Ural Mathematical Journal, 2021 Let \({E}_{n}\) be the ring of Eisenstein integers modulo \(n\). We denote by \(G({E}_{n})\) and \(G_{{E}_{n}}\), the unit graph and the unitary Cayley graph of \({E}_{n}\), respectively. In this paper, we obtain the value of the diameter, the girth, the
Reza Jahani-Nezhad, Ali Bahrami
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(Random) Trees of Intermediate Volume Growth
Random Structures &Algorithms, Volume 67, Issue 4, December 2025.ABSTRACT For every function g:ℝ≥0→ℝ≥0$$ g:{\mathbb{R}}_{\ge 0}\to {\mathbb{R}}_{\ge 0} $$ that grows at least linearly and at most exponentially, if it is sufficiently well‐behaved, we can construct a tree T$$ T $$ of uniform volume growth g$$ g $$, or more precisely, C1·g(r/4)≤|BG(v,r)|≤C2·g(4r),for allr≥0andv∈V(T),$$ {C}_1\cdotp g\left(r/4\right)\le \
George Kontogeorgiou, Martin Winter
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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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Perfect Codes in Cayley Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2018 This is the final version that will appear in SIAM J.
Huang, He, Xia, Binzhou, Zhou, Sanming
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