Indonesian Journal of Combinatorics
Vol 6, No 1 (2022)

The local metric dimension of split and unicyclic graphs

Dinny Fitriani (Institut Teknologi Bandung)
Anisa Rarasati (Institut Teknologi Bandung)
Suhadi Wido Saputro (Institut Teknologi Bandung)
Edy Tri Baskoro (Institut Teknologi Bandung)

Article Info

Publish Date
28 Jun 2022

Abstract

A set W is called a local resolving set of G if the distance of u and v to some elements of W are distinct for every two adjacent vertices u and v in G.  The local metric dimension of G is the minimum cardinality of a local resolving set of G.  A connected graph G is called a split graph if V(G) can be partitioned into two subsets V1 and V2 where an induced subgraph of G by V1 and V2 is a complete graph and an independent set, respectively.  We also consider a graph, namely the unicyclic graph which is a connected graph containing exactly one cycle.  In this paper, we provide a general sharp bounds of local metric dimension of split graph.  We also determine an exact value of local metric dimension of any unicyclic graphs.

Copyrights © 2022




Citation Download
RIS
EndNote, Reference Manager, ProCite
BibTex
Latex, Jabref
Original Source
Download Original
Google Scholar
Check in Google Scholar
Journal Info
Indonesian Journal of Combinatorics
Website

Abbrev

ijc

Publisher

Indonesian Combinatorial Society

Subject

Computer Science & IT Decision Sciences, Operations Research & Management

Description

Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian ...