Edge-locating coloring of graphs
| Main Authors: | Korivand, Meysam; Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran, Mojdeh, Doost Ali; Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran, Baskoro, Edy Tri; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia, Erfanian, Ahmad; Department of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence in Analysis on Algebraic Structures Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2024
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/2011 https://www.ejgta.org/index.php/ejgta/article/view/2011/pdf_300 https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/2011/466 |
Daftar Isi:
- An edge-locating coloring of a simple connected graph G is a partition of its edge set into matchings such that the vertices of G are distinguished by the distance to the matchings. The minimum number of the matchings of G that admits an edge-locating coloring is the edge-locating chromatic number of G, and denoted by χ′L(G). This paper introduces and studies the concept of edge-locating coloring. Graphs G with χ′L(G)∈{2, m} are characterized, where m is the size of G. We investigate the relationship between order, diameter and edge-locating chromatic number. We obtain the exact values of χ′L(Kn) and χ′L(Kn − M), where M is a maximum matching; indeed this result is also extended for any graph. We determine the edge-locating chromatic number of the join graphs of some well-known graphs. In particular, for any graph G, we show a relationship between χ′L(G + K1) and Δ(G). We investigate the edge-locating chromatic number of trees and present a characterization bound for any tree in terms of maximum degree, number of leaves, and the support vertices of trees. Finally, we prove that any edge-locating coloring of a graph is an edge distinguishing coloring.