梁志和.关于奇算术图[J].数学研究及应用,2008,28(3):706~712 |
关于奇算术图 |
On Odd Arithmetic Graphs |
投稿时间:2006-05-30 修订日期:2007-05-23 |
DOI:10.3770/j.issn:1000-341X.2008.03.035 |
中文关键词: 奇算术编码 星形图 完全图 圈. |
英文关键词:odd arithmetic graph complete graph cycle graph $C^n_m\cdot P_t$. |
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中文摘要: |
本文讨论了$n$个$m$长圈有一个公共结点图$C^n_m$, $n$个$m$长圈与$t$长路有一个公共结点图$C^n_m\cdot P_t$, $n$个$m$阶完全图有一个公共结点图$K^n_m$和星形图的同胚图的奇算术性问题.给出了完全图,完全二部图和圈是奇算术的充要条件. |
英文摘要: |
The following results are obtained: (1) The graph $C^n_m\cdot P_t$ is odd arithmetic when (i) $m\equiv 0$ (mod 2) and $t$=$m$ or$m+1$; (ii) $m\equiv 1$ (mod 2) and $t$=$m+1$. (2) The graph$C^n_{2m}$ is odd arithmetic when (i) $m$=2,4 and $n$ is any positive integer; (ii) $m$=3 and $n$ is even. (3) The graph $C_{m}^n$ is odd arithmetic when $m$=$4n$ and $t$=2. (4) $P_{m+1}^n$ is odd arithmetic when (i) $n$ is odd; (ii) $m\leq 3$ and $n$ is any positive integer. (5) Windmill graph $K_n^t$ is odd arithmetic if and only if $n$=2. (6) Cycle $C_n$ is odd arithmetic if and only if $n\equiv 0$ (mod 4). (7) For any positive integer $n$ and any positive integer $m$, $K_{m,n}$ is odd arithmetic. |
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