由圈长分布确定的二部图K_(n,n+r)-A(︱A︱≤3)(英文)

摘要

The cycle length distribution of a graph G of order n is a sequence(c1(G),...,cn(G)),where ci(G) is the number of cycles of length i in G.In general,the graphs with cycle length distribution(c1(G),...,cn(G)) are not unique.A graph G is determined by its cycle length distribution if the graph with cycle length distribution(c1(G),...,cn(G)) is unique.Let Kn,n+r be a complete bipartite graph and A■E(Kn,n+r).In this paper,we obtain:Let s>1 be an integer.(1) If r=2s,n>s(s-1)+2|A|,then Kn,n+r-A(A■E(Kn,n+r),|A|≤3) is determined by its cycle length distribution;(2) If r=2s+1,n>s 2+2|A|,Kn,n+r-A(A■E(Kn,n+r),|A|≤3) is determined by its cycle length distribution.