Local multiset dimension of corona product on tree graphs

Abstract

One of the topics of distance in graphs is resolving set problem. This topic has many applications in science and technology namely navigation robots, chemistry structure, and computer sciences. Suppose the set [Formula: see text], the vertex representations of [Formula: see text] is [Formula: see text], where [Formula: see text] is the length of the shortest path of the vertex [Formula: see text] and the vertex in [Formula: see text] together with their multiplicity. The set W is called a local [Formula: see text]-resolving set of graphs G if [Formula: see text] for [Formula: see text]. The local [Formula: see text]-resolving set having minimum cardinality is called the local multiset basis and its cardinality is called the local multiset dimension of [Formula: see text], denoted by [Formula: see text]. In our paper, we determine the establish bounds of local multiset dimension of graph resulting corona product of tree graphs.