Book Title: Contemporary Research Across Disciplines
Editors: Dr. R. Saravana Selvakumar and Mr. R. Venkatesan
ISBN: 978-81-978738-1-2
Chapter: 22
DOI: https://doi.org/10.59646/crc22/278
Author: Dr. N. Shunmuga Priya, Assistant Professor, PG & Research Department of Mathematics, G. Venkataswamy Naidu College (Autonomous), Kovilpatti, Tamil Nadu, India
Abstract
In this paper, we investigate the total resolving number of edge cycle graphs G(C3) G (C_3) G (C3). When their edge cycle graphs are considered, we determine the exact values for the total resolving number for trees, cycles, and friendship graphs. We also establish general bounds for the total resolving number of G(C3) G(C_3) G(C3) and characterize extremal graphs that achieve these bounds. Our results contribute to a deeper understanding of graph theory’s metric dimension and total resolving sets, particularly for edge cycle graphs.
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