The local multiset dimension of graphs - Alfarisi, Ridho; ., Dafik; Indah Kristiana, Arika; Hesti Agustin, Ika (International Journal of Engineering and Technology, 2019)
All graphs in this paper are nontrivial and connected graph. For -ordered set Â of vertex set , the multiset representation of a vertex Â of Â with respect to Â is Â where Â is a distance between of the vertex Â and the vertices in Â together with their multiplicities. The resolving set Â is a local resolving set of Â if Â for every pair Â of adjacent vertices of . The minimum local resolving set Â is a local multiset basis of . If Â has a local multiset basis, then its cardinality is called local multiset dimension,denoted by . If Â does not contain a local resolving set, then we write Â In our paper, we will investigate the establish sharp bounds of the local multiset dimension of Â and determine the exact value of some family graphs.