Results 51 to 60 of about 22,931 (240)
A tropical approach to rigidity: Counting realisations of frameworks
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A realisation of a graph in the plane as a bar‐joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points.
Oliver Clarke +6 more
wiley +1 more source
Discrete Mathematics, 1992 The autors introduce the concept of generalized Cayley graph. The main result is that if \(X\) is a graph, \(B(X)\) its double covering then \(B(X)\) is a Cayley graph if and only if \(X\) is a generalized Cayley graph. Another result is that a generalized Cayley graph that is stable is a Cayley graph. Furthermore a construction is given of a family of
MARUSIC D. +2 more
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Nearly Hamilton cycles in sublinear expanders and applications
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We develop novel methods for constructing nearly Hamilton cycles in sublinear expanders with good regularity properties, as well as new techniques for finding such expanders in general graphs. These methods are of independent interest due to their potential for various applications to embedding problems in sparse graphs.
Shoham Letzter +2 more
wiley +1 more source
Random Structures &Algorithms, Volume 68, Issue 1, January 2026.ABSTRACT We study a random walk on the Lie algebra sl2(Fp)$$ {\mathfrak{sl}}_2\left({\mathbf{F}}_p\right) $$ where new elements are produced by randomly applying adjoint operators of two generators. Focusing on the generic case where the generators are selected at random, we analyze the limiting distribution of the random walk and the speed at which it
Urban Jezernik, Matevž Miščič
wiley +1 more source
Cayley Graphs Defined by Systems of Equations
Axioms, 2022 Let R be a finite ring. In this paper, we mainly explore the conditions to ensure the graph BΓn defined by a system of equations {fi|i=2,…,n} to be a Cayley graph or a Hamiltonian graph.
Fuyuan Yang +3 more
doaj +1 more source
Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups [PDF]
, 2012 It is shown that distance powers of an integral Cayley graph over an abelian group are again integral Cayley graphs over that group. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral ...
Klotz, W., Sander, T.
core
Residually rationally solvable one‐relator groups
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract We show that the intersection of the rational derived series of a one‐relator group is rationally perfect and is normally generated by a single element. As a corollary, we characterise precisely when a one‐relator group is residually rationally solvable.
Marco Linton
wiley +1 more source
Coloring minimal Cayley graphs
European Journal of Combinatorics9 pages, 1 ...
García Marco, Ignacio, Knauer, Kolja
openaire +4 more sources
Strongly Regular Semi-Cayley Graphs [PDF]
Journal of Algebraic Combinatorics, 1992 This paper studies strongly regular graphs \(G\) on \(2n\) vertices which admit a group of automorphisms \(\Gamma\) of order \(n\) with two orbits of length \(n\) on the vertices of \(G\), which are called semi-Cayley graphs. The Petersen and Hoffman-Singleton graphs provide examples.
de Resmini, Marialuisa J. +1 more
openaire +3 more sources
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