Uniqueness of Cycle Length Distributions of Certain Bipartite Graphs $K_{n,n+7}-A(|A|\leq3)$ |
Received:November 13, 2006 Revised:March 23, 2007 |
Key Words:
cycle cycle length distribution bipartite graph uniqueness of cycle length distribution.
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Fund Project:the Science Foundation of Shanghai Municipal Education Commission (No.04DB25). |
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Abstract: |
The cycle length distribution of a graph of order $n$ is denoted by $(c_1,c_2,\ldots,c_n)$, where $c_i$ is the number of cycles of length $i$. In this paper, we obtain that a graph $G$ is uniquely determined by its cycle distribution if: (1) $G=K_{n,n+7}$ $(n\geq10)$; or (2) $G=K_{n,n+7}-A~(|A|=1,n\geq12)$; or (3) $G=K_{n,n+7}-A~(|A|=2,n\geq14)$; or (4) $G=K_{n,n+7}-A~(|A|=3,n\geq16)$, where $A\subseteq E(K_{n,n+7})$. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2008.04.009 |
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