Results of Paired Domination of Some Special Graph Families on Transformation Graphs: $G^{xy+}$ and $G^{xy-}$

Author:

TUNÇEL GÖLPEK Hande1ORCID

Affiliation:

1. DOKUZ EYLUL UNIVERSITY

Abstract

In this study, transformation graphs obtained from the concept of the total graph and the result of its paired domination number for some special graph families are discussed. If a subset $S$ of the vertex set of the graph $G$ dominates and the induced subgraph $⟨S⟩$ has a perfect matching that covers every vertex of the graph, then $S$ is called a paired-dominating set of $G$. A paired dominating set with the smallest cardinality is denoted by $\gamma_{pr}$-set. Haynes and Slater introduced paired domination parameters. The present study commences with assessing outcomes stemming from eight permutations within the realm of path graphs. Subsequently, building upon this foundational structure, the results are extrapolated from the realm of cycle transformation graph structures based on findings from path transformation graphs.

Publisher

Gaziosmanpasa University

Subject

Geology,Ocean Engineering,Water Science and Technology

Reference26 articles.

1. E. J. Cockayne, R. M. Dawes, S. T. Hedetniemi, Total Domination in Graphs, Networks 10 (3) (1980) 211-219.

2. T. W. Haynes, P. J. Slater, Paired-Domination in Graphs, Networks 32 (3) (1998) 199-206.

3. W. J. Desormeaux, M. A. Henning, Paired Domination in Graphs: A Survey and Recent Results, Utilitas Mathematica 94 (2014) 101–166.

4. M. Chellali, T. W. Haynes, Total and Paired-Domination Numbers of a Tree, AKCE International Journal of Graphs and Combinatorics 1 (2) (2004) 69–75.

5. A. D. Gray, M. A. Henning, Paired-Domination Game Played on Cycles, Discrete Applied Mathematics 336 (2023) 132–140.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3