On local adjacency metric dimension of some wheel related graphs with pendant points

Rinurwati, Herry Suprajitno, Slamin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Citations (Scopus)

Abstract

Let G = (V(G),E(G)) be any connected graph of order n = |V(G)| and measure m = |E(G)|. For an order set of vertices S = { s1, s2, ..., sk} and a vertex v in G, the adjacency representation of v with respect to S is the ordered k-tuple rA(v|S) = (dA(v, s1), dA(v, s2), ..., dA(v, sk)), where dA(u,v) represents the adjacency distance between the vertices u and v. The set S is called a local adjacency resolving set of G if for every two distinct vertices u and v in G, u adjacent v then rA(u|S)≠rA(v|S). A minimum local adjacency resolving set for G is a local adjacency metric basis of G. Local adjacency metric dimension for G, dimA,l(G), is the cardinality of vertices in a local adjacency metric basis for G. In this paper, we study and determine the local adjacency metric dimension of some wheel related graphs G (namely gear graph, helm, sunflower and friendship graph) with pendant points, that is edge corona product of G and a trivial graph K1, G⋄K1. Moreover, we compare among the local adjacency metric dimension of G⋄K1 graph,of Wn⋄K1 graph and metric dimension of Wn.

Original languageEnglish
Title of host publicationInternational Conference on Mathematics - Pure, Applied and Computation
Subtitle of host publicationEmpowering Engineering using Mathematics
EditorsDieky Adzkiya
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735415478
DOIs
Publication statusPublished - 1 Aug 2017
Externally publishedYes
Event2nd International Conference on Mathematics - Pure, Applied and Computation: Empowering Engineering using Mathematics, ICoMPAC 2016 - Surabaya, Indonesia
Duration: 23 Nov 2016 → …

Publication series

NameAIP Conference Proceedings
Volume1867
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference2nd International Conference on Mathematics - Pure, Applied and Computation: Empowering Engineering using Mathematics, ICoMPAC 2016
Country/TerritoryIndonesia
CitySurabaya
Period23/11/16 → …

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