一类特殊笛卡尔乘积网络的圈因子分解  

Cycle Factor Decomposition of a Special Cartesian Product Network

作　　者：何巧玲 张治成 HE Qiao-ling;ZHANG Zhi-cheng(College of Science,Shihezi University,Shihezi 832003,China)

机构地区：[1]石河子大学理学院,新疆石河子832003

出　　处：《数学的实践与认识》2021年第24期298-303,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11861054)。

摘　　要：圈分解是图论中研究的重点问题之一.图G能分解成若干个圈的和,则称图G是圈因子可分解的,也称为是2因子可分解的.文章在引理1和2的基础上,推广得到任一2m阶的Hamilton平面图G与K_(2)的笛卡尔乘积网络G×K_(2)中存在1到m圈的2-因子,且进一步给出笛卡尔乘积网络DSCC(k)×K_(2)(k≥1)中存在1到40×3^(k-1)圈的2-因子.Cyclic decomposition is one of the most important problems in graph theory.If a graph G can be decomposed into a sum of several cycles,it is called that the graph G is cycle factor decomposable,or is also called 2-factorable decomposable.Based on Lemma 1 and 2,this paper generalizes the existence of 2-factors from 1 to m cycles in the Cartesian product network G×K_(2)of any 2 m order Hamiltonian plane graph G and K_(2),and further gives the existence of 2 factors from 1 to 40×3^(k-1)cycles in the DSCC(k)×K_(2)(k≥1)of Cartesian product network.

关 键 词：笛卡尔乘积网络 圈因子分解 2-因子 DSCC(k)×K HAMILTON图 

分 类 号：O157.5[理学—数学]