Let V (G) be the vertex set of a simple and connected graph G. A subset S⊆ V (G) is a
distance-equalizer set of G if, for every pair of vertices u, v∈ V (G)\S, there exists a vertex in …

In this paper the recently introduced concept of equidistant dimension $ eqdim (G) $ of
graph $ G $ is considered. Useful property of distance-equalizer set of arbitrary graph $ G …

Let Γ denote a bipartite graph with vertex set X and color partitions Y, Y′. For a nonnegative
integer i and a vertex x∈ X, let Γ i (x) denote the set of vertices in X that are at distance i from …

A Roman domination function (RDF) on a graph G with a set of vertices V= V (G) is a function
f: V→{0, 1, 2} which satisfies the condition that each vertex v∈ V such that f (v)= 0 is adjacent …

In this paper, both edge and mixed metric dimensions of Johnson graphs $ J_ {n, k} $ are
considered. A new tight lower bound for $\beta_E (J_ {n, k}) $ based on hitting sets has been …

This paper is devoted to some rotationally symmetric classes of graphs denoted in literature
as convex polytope graphs. Exact value of equidistant dimension is found for $ T_n $. Next …