Outer multiset dimension of joined graphs - Hassan Pervaiz; Rinovia Simanjuntak; Suhadi Wido Saputro (Indonesian Journal of Combinatorics, 2025)
The outer multiset dimension of graph G, dimms(G), is the cardinality of the smallest subset S of vertices that uniquely recognizes each vertex outside S by using the multiset of distances between the vertex and the vertices in S. In 2023, Klavzar, Kuziak, and Yero proved that the only graphs with the largest outer multiset dimension, that is, one less than their order, are regular graphs of diameter at most 2. This paper considers the outer multiset dimensions of non-regular graphs of diameter 2 obtained from the join product, in particular, stars, wheels, generalized wheels, windmills, fans, and generalized fans.