摘要
Let G be a finite simple graph and A(G)be its adjacency matrix.Then G is singular if A(G)is singular.The graph obtained by bonding the starting ver-tices and ending vertices of three paths Pa1,Pa2,Pa3 is calledθ-graph,represented byθ(a1,a2,a3).The graph obtained by bonding the two end vertices of the path Ps to the vertices of theθ(a1,a2,a3)andθ(b1,b2,b3)of degree three,respectively,is denoted byα(a1,a2,a3,s,b1,b2,b3)and calledα-graph.β-graph is denoted whenβ(a1,a2,a3,b1,b2,b3)=α(a1,a2,a3,1,b1,b2,b3).In this paper,we give the necessary and sufficient conditions for the singularity ofα-graph andβ-graph,and prove that the probability that a random givenα-graph andβ-graph is a singular graph is equal to 14232048 and 733/1024,respectively.
作者
攸晓杰
马海成
张斌
李雅兰
YOU Xiao-jie;MA Hai-cheng;ZHANG Bin;LI Ya-lan(School of Mathematics and Statistics,Qinghai Minzu University,Xining 810007,China;School of Mathematics and Statistics,Qinghai Normal University,Xining 810008,China)
基金
Supported by National Natural Science Foundation of China(Grant No.11561056)
National Natural Science Foundation of Qinghai Provence(Grant No.2022-ZJ-924)
Innovation Project of Qinghai Minzu University(Grant No.07M2022002).
