Alje Marie M. Urenda, Jacel Angeline V. Lingcong, Normina A. Batucan, Joel G. Adanza, Michael P. Baldado Jr.
{"title":"Packing chromatic number of the join of some classes of graphs","authors":"Alje Marie M. Urenda, Jacel Angeline V. Lingcong, Normina A. Batucan, Joel G. Adanza, Michael P. Baldado Jr.","doi":"10.12988/imf.2022.912315","DOIUrl":null,"url":null,"abstract":"Let G be a graph. A packing k-coloring of G is a function f : V (G)→ {1, 2, . . . , k} such that any two vertices of color i are at a distance at least i + 1. The packing chromatic number of G, denoted by χρ(G), is the smallest integer k for which there exists a packing k-coloring f : V (G)→ {1, 2, . . . , k}. In this paper, we gave the packing chromatic number of the join of some classes of graphs. Moreover, we characterized graphs with packing chromatic number equal to their order. Mathematics Subject Classification: 05C15","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/imf.2022.912315","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let G be a graph. A packing k-coloring of G is a function f : V (G)→ {1, 2, . . . , k} such that any two vertices of color i are at a distance at least i + 1. The packing chromatic number of G, denoted by χρ(G), is the smallest integer k for which there exists a packing k-coloring f : V (G)→ {1, 2, . . . , k}. In this paper, we gave the packing chromatic number of the join of some classes of graphs. Moreover, we characterized graphs with packing chromatic number equal to their order. Mathematics Subject Classification: 05C15
设G是一个图。G的填充k-着色是一个函数f: V (G)→{1,2，…， k}使得任意两个颜色为I的顶点之间的距离至少为I + 1。G的填充色数，用χρ(G)表示，是存在填充k-着色f: V (G)→{1,2，…的最小整数k。k}。本文给出了几类图的连接的填充色数。此外，我们还刻画了图的填充色数等于其阶数。数学学科分类:055c15
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
