广义太阳图与路的笛卡儿积图的任意可分性  

Partitioning the Cartesian Product of Generalized Sun-Like Graph and Path

作　　者：西日尼阿依·努尔麦麦提 张盼盼 刘凤霞[1] 孟吉翔[1] Xirinay Nurmamat;ZHANG Panpan;LIU Fengxia;MENG Jixiang(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）（中英文）》2021年第5期549-555,共7页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金项目(11961067,11531011).

摘　　要：给定n个顶点的图G.如果对于n的满足∑_(i=1)^(k)n_(i)=n的任意一个正整数序列τ=(n_(1),n_(2),···,n_(k)),都存在顶点集V(G)的划分(V_(1),V_(2),···,V_(k))满足|V_(i)|=n_(i),并且Vi导出的子图G[V_(i)]是连通的,其中1≤i≤k,则称图G是任意可分图(简称为AP).我们用S^(**)=S(n;k_(1),k_(2),···,k_(n))来表示一类广义太阳图.本文主要讨论图类S^(**)□Pm的任意可分性.An n-vertex graph G is called arbitrarily partitionable(AP,for short),if for any sequenceτ=(n_(1),n_(2),···,n_(k))of positive integers such that ∑_(i=1)^(k)n_(i)=n,there exists a partition(V_(1),V_(2),···,V_(k))of the vertex set V(G)such that for all 1≤i≤k,|V_(i)|=n_(i) and the subgraph G[Vi]induced by V_(i) is connected.We use S^(**)=S(n;k_(1),k_(2),···,k_(n))to denote the generalized sun-like graph.In this paper,we mainly discuss the arbitrary partitionability of graph S^(**)□Pm.

关 键 词：任意可分图 笛卡儿积图 广义太阳图 可迹图 

分 类 号：O157.5[理学—数学]