Strong Domination Index in Fuzzy Graphs

被引：1

作者：

Nair, Kavya R. ^{[1
]}

Sunitha, Muraleedharan Shetty ^{[1
]}

机构：

[1] Natl Inst Technol, Dept Math, Calicut 673601, India

来源：

FUZZY INFORMATION AND ENGINEERING | 2024年 / 16卷 / 01期

关键词：

strong domination degree; strong domination regular fuzzy graph (FG); strong domination index; upper strong domination number; strong irredundance number; strong upper irredundance number; strong independent domination number; strong independence number; r-partite FG; TOPOLOGICAL INDEXES; INDEPENDENCE;

D O I：

10.26599/FIE.2023.9270028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a novel idea of domination degree and index are defined in a fuzzy graph (FG) using weight of strong edges. The strong domination degree (SDD) of a vertex u is defined using the weight of minimal strong dominating set (MSDS) containing u. Methods to obtain an MSDS containing a particular vertex are discussed in the article. Idea of upper strong domination number, strong irredundance number, strong upper irredundance number, strong independent domination number, and strong independence number are explained and illustrated subsequently. Strong domination index (SDI) of an FG is defined using the SDD of each vertex. The concept is applied on various FGs like complete FG, complete bipartite and r-partite FG, fuzzy tree, fuzzy cycle, and fuzzy stars. Bounds involving the SDD and SDI are also obtained. Applications for SDD of a vertex is also provided.

引用

页码：1 / 23

页数：23