图中的$J^2$-Hop支配:与其他参数的性质和联系

IF 1 Q1 MATHEMATICS
Javier Hassan, Alcyn R. Bakkang, Amil-Shab S. Sappari
{"title":"图中的$J^2$-Hop支配:与其他参数的性质和联系","authors":"Javier Hassan, Alcyn R. Bakkang, Amil-Shab S. Sappari","doi":"10.29020/nybg.ejpam.v16i4.4905","DOIUrl":null,"url":null,"abstract":"A subset $T=\\{v_1, v_2, \\cdots, v_m\\}$ of vertices of an undirected graph $G$ is called a $J^2$-set if$N_G^2[v_i]\\setminus N_G^2[v_j]\\neq \\varnothing$ for every $i\\neq j$, where $i,j\\in\\{1, 2, \\ldots, m\\}$.A $J^2$-set is called a $J^2$-hop dominating in $G$ if for every $a\\in V(G)\\s T$, there exists $b\\in T$ such that $d_G(a,b)=2$. The $J^2$-hop domination number of $G$, denoted by $\\gamma_{J^2h}(G)$, is the maximum cardinality among all $J^2$-hop dominating sets in $G$. In this paper, we introduce this new parameter and wedetermine its connections with other known parameters in graph theory. We derive its bounds with respect to the order of a graph and other known parameters on a generalized graph, join and corona of two graphs. Moreover,we obtain exact values of the parameter for some special graphs and shadow graphs using the characterization results that are formulated in this study.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$J^2$-Hop Domination in Graphs: Properties and Connections with Other Parameters\",\"authors\":\"Javier Hassan, Alcyn R. Bakkang, Amil-Shab S. Sappari\",\"doi\":\"10.29020/nybg.ejpam.v16i4.4905\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A subset $T=\\\\{v_1, v_2, \\\\cdots, v_m\\\\}$ of vertices of an undirected graph $G$ is called a $J^2$-set if$N_G^2[v_i]\\\\setminus N_G^2[v_j]\\\\neq \\\\varnothing$ for every $i\\\\neq j$, where $i,j\\\\in\\\\{1, 2, \\\\ldots, m\\\\}$.A $J^2$-set is called a $J^2$-hop dominating in $G$ if for every $a\\\\in V(G)\\\\s T$, there exists $b\\\\in T$ such that $d_G(a,b)=2$. The $J^2$-hop domination number of $G$, denoted by $\\\\gamma_{J^2h}(G)$, is the maximum cardinality among all $J^2$-hop dominating sets in $G$. In this paper, we introduce this new parameter and wedetermine its connections with other known parameters in graph theory. We derive its bounds with respect to the order of a graph and other known parameters on a generalized graph, join and corona of two graphs. Moreover,we obtain exact values of the parameter for some special graphs and shadow graphs using the characterization results that are formulated in this study.\",\"PeriodicalId\":51807,\"journal\":{\"name\":\"European Journal of Pure and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29020/nybg.ejpam.v16i4.4905\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29020/nybg.ejpam.v16i4.4905","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

子集 $T=\{v_1, v_2, \cdots, v_m\}$ 一个无向图的顶点 $G$ 叫做a $J^2$-set if$N_G^2[v_i]\setminus N_G^2[v_j]\neq \varnothing$ 对于每一个 $i\neq j$,其中 $i,j\in\{1, 2, \ldots, m\}$a $J^2$-set称为a $J^2$-跳跃支配 $G$ 如果对于每一个 $a\in V(G)\s T$,存在 $b\in T$ 这样 $d_G(a,b)=2$. The $J^2$-hop支配数 $G$,表示为 $\gamma_{J^2h}(G)$,是所有集合中的最大基数 $J^2$-跳跃支配开始了 $G$. 本文引入了这个新参数,并确定了它与图论中其他已知参数的联系。在广义图上,我们推导了它关于图的阶和其他已知参数的界,以及两个图的连接和电晕。此外,我们还利用本文所建立的表征结果,获得了一些特殊图和阴影图的精确参数值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
$J^2$-Hop Domination in Graphs: Properties and Connections with Other Parameters
A subset $T=\{v_1, v_2, \cdots, v_m\}$ of vertices of an undirected graph $G$ is called a $J^2$-set if$N_G^2[v_i]\setminus N_G^2[v_j]\neq \varnothing$ for every $i\neq j$, where $i,j\in\{1, 2, \ldots, m\}$.A $J^2$-set is called a $J^2$-hop dominating in $G$ if for every $a\in V(G)\s T$, there exists $b\in T$ such that $d_G(a,b)=2$. The $J^2$-hop domination number of $G$, denoted by $\gamma_{J^2h}(G)$, is the maximum cardinality among all $J^2$-hop dominating sets in $G$. In this paper, we introduce this new parameter and wedetermine its connections with other known parameters in graph theory. We derive its bounds with respect to the order of a graph and other known parameters on a generalized graph, join and corona of two graphs. Moreover,we obtain exact values of the parameter for some special graphs and shadow graphs using the characterization results that are formulated in this study.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信