The local multiset dimension of graphs

Ridho Alfarisi; Dafik .; Arika Indah Kristiana; Ika Hesti Agustin

doi:10.14419/ijet.v8i3.11643

Authors

Ridho Alfarisi University of Jember
Dafik . University of Jember
Arika Indah Kristiana University of Jember
Ika Hesti Agustin University of Jember

DOI:

https://doi.org/10.14419/ijet.v8i3.11643

Published:

2019-08-25

Keywords:

Local Resolving Set, Local Multiset Dimension, Distance, Some Family Graph.

Abstract

All graphs in this paper are nontrivial and connected graph. For -ordered set of vertex set , the multiset representation of a vertex of with respect to is where is a distance between of the vertex and the vertices in together with their multiplicities. The resolving set is a local resolving set of if for every pair of adjacent vertices of . The minimum local resolving set is a local multiset basis of . If has a local multiset basis, then its cardinality is called local multiset dimension,denoted by . If does not contain a local resolving set, then we write In our paper, we will investigate the establish sharp bounds of the local multiset dimension of and determine the exact value of some family graphs.

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