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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Saputro, Suhadi Wido
Dept. of Mathematics of ITB
Electrical & Electronics Engineering

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The local metric dimension of amalgamation of graphs Fitriani, Dinny; Saputro, Suhadi Wido
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.1.11

Abstract

For any two adjacent vertices u and v in graph G, a set of vertices W locally resolves a graph G if the distance of u and v to some elements of W are distinct. The local metric dimension of G is the minimum cardinality of local resolving sets of G. For n ∈ N and i ∈ {1, 2, …, n}, let Hi be a simple connected graph containing a connected subgraph J. Let H = {H1, H2, …, Hn} be a finite collection of simple connected graphs. The subgraph-amalgamation of H = {H1, H2, …, Hn}, denoted by Subgraph − Amal{H; J}, is a graph obtained by identifying all elements of H in J. The subgraph J is called as a terminal subgraph of H. In this paper, we determine general bounds of the local metric dimension of subgraph-amalgamation graphs for any connected terminal subgraphs. We also determine the local metric dimension of Subgraph − Amal{H; J} for J is either K1 or P2.
Co-Authors Fitriani, Dinny