The minimum number of colors required to color the edges of a graph so that any two distinct vertices are connected by at least one path in which no two edges are colored the same is called its rainbow connection number. This graph parameter was introduced by Chartrand et al. in 2008. The problem has garnered considerable interest and several variants of the initial version have since been intr...

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (Note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely cartesian p...

Harmonic centrality calculates the importance of a node in network by adding inverse geodesic distances this to all other nodes. centralization, on hand, is graph-level score based node-level harmonic centrality. In paper, we present some results both and centralization graphs resulting from graph products such as Cartesian direct path $P_2$ with any $P_m$, cycle $C_m$, fan $F_m$ graphs.