On the star partition dimension of comb product of cycle and complete graph

Abstract

Abstract. Let G = (V, E) be a connected graphs with vertex set V (G), edge set E(G) andwhere d(v, S k ) represents the distance between the vertex v and the set S k , defined byThe minimum resolving partition Π is a partition dimension of G, denoted by pd(G). The resolving partition Π = {S1, S2, S3, . . . , S k } is called a star resolving partition for G if it is a resolving partition and each subgraph induced by Si, 1 ≤ i ≤ k, is a star. The minimum k for which there exists a star resolving partition of V (G)

On the Bounded Partition Dimension of Some Generalised Graph Structures

“…Te concept of resolving set was introduced by the authors of [2] and later introduced by the authors of [3]. In [4], the authors worked on the star partition dimension of the cycle and complete graph by using a comb product. Authors worked on the partition dimension of diferent classes of circulant graph [5].…”

On Star Coloring of Degree Splitting of Comb Product Graphs

“…Let G and H be two connected graphs. Let o be a vertex of H. The comb product between G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the i th copy of H at the vertex o to the i th vertex of G. By the definition of comb product, we can say that V (G⊲ [2] determined the partition dimension of comb product of path and complete graph and in [7] they also determined the star partition dimension of comb product of cycle and complete graph. Saputro et al showed the metric dimension of comb product of the connected graphs G and H in [13].…”