Isolate g-eccentric domination in fuzzy graph

Authors

  • S. Muthupandiyan Research Scholar (Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan Universty), Tiruchirappalli-620020, Tamilnadu, India)
  • A Mohamed Ismayil Associate Professor (Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan Universty), Tiruchirappalli-620020, Tamilnadu, India);

DOI:

https://doi.org/10.23755/rm.v50i0.1548

Keywords:

Fuzzy graph(FG), g-Distance, Isolate g-eccentric number, Isolate domination number, g-eccentric domination number, Isolate g-eccentric domination number.

Abstract

In a fuzzy graph G(ρ, μ), a dominating set D ⊆ P(G) is said to be g-eccentric if at least one g-eccentric vertex a of every vertex b in P − D exists in D. If the induced fuzzy sub graph < D > has at least one isolated vertex, then a g-eccentric dominating set D of G is said to be an isolate g-eccentric dominating set. The isolate g-eccentric domination number is defined as the smallest cardinality over all isolate g-eccentric dominating sets of G. This article introduces the isolate g-eccentric point set, isolate g-eccentric dominating set, and their numbers in fuzzy graphs. In some standard fuzzy graphs, bounds are found for an isolate g-eccentric domination number.

Author Biographies

  • S. Muthupandiyan, Research Scholar (Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan Universty), Tiruchirappalli-620020, Tamilnadu, India)

    Research Scholar (Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan Universty), Tiruchirappalli-620020, Tamilnadu, India);

  • A Mohamed Ismayil, Associate Professor (Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan Universty), Tiruchirappalli-620020, Tamilnadu, India);

    Associate Professor (Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan Universty), Tiruchirappalli-620020, Tamilnadu, India)

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Published

2023-12-29

Issue

Vol. 50 (2023): SPECIAL ISSUE: RECENT INNOVATIONS IN APPLICATIONS OF MATHEMATICS

Section

Volume 50-2023

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