On Unimodular Matrix Representation of the Automorphism Group of a Graph
摘要
Recently,Estélyi et al.investigated a representation ΘT of the automorphisms of a connected graph X by β × β unimodular matrices over {0,±1},where β is the Betti number of X,and classified the graphs for which the representation is unfaithful,with two problems left open:(1)What is the smallest dimension d such that AutX is faithfully represented by d × d unimodular matrices?(2)Given a finite group G,find the smallest graph X such that G ≤ AutX is faithfully represented by unimodular matrices.In this article,we prove that AutX has a faithful representation by unimodular matrices of dimension d＜β if every major vertex of X has at least four subneighbors.We also classify the graphs X with Betti number β for which the image of Aut X under ΘT has a subgroup isomorphic to the symmetry group on β elements.
年，卷(期)：
2026, 33(2)
分类号：
05C50
05C25
机标分类号：
TP18
P208
C912
在线出版日期：
2026年7月17日
