Weighted PI index of corona product of graphs

Abstract

In this paper, we present exact formula for the weighted PI index of corona product of two connected graphs in terms of other graph invariants including the PI index, first Zagreb index and second Zagreb index. Then, we apply our result to compute the weighted PI indices of t-fold bristled graph, bottleneck graph, sunlet graph, star graph, fan graph, wheel graph and some classes of bridge graphs.

Reformulated First Zagreb Index of Some Graph Operations

“…Clearly, the corona product operation of two graphs is not commutative. Different topological indices of the corona product of two graphs have already been studied in [24,25]. Let the vertices of G 1 be denoted by V (G 1 ) = u 1 , u 2 , ..., u |V (G 1 )| and the vertices of the i-th copy of G 2 are denoted by V (G …”

The vertex Zagreb indices of some graph operations

“…Thus, the corona product of G 1 and G 2 has total (n 1 n 2 + n 1 ) number of vertices and (m 1 + n 1 m 2 + n 1 n 2 ) number of edges. A variety of topological indices under the corona product of graphs have already been studied by researchers [24,26]. The degree of a vertex v of G 1 • G 2 is given by…”

Modified Eccentric Connectivity Index and Polynomial of Corona Product of Graphs

“…Now we consider three particular type of bridge graphs as in [24,2,18], named as B n = G n (P 3 , v), T m,k = G m (C k , u) and J n,m+1 = G n (P 3 , v). According to definition of corona product of graphs the bridge graphs B n = P n • K 2 , T m,3 = P m • K 2 and J n,m+1 = P n • C m .…”

“…Clearly, the corona product operation of two graphs is not commutative. Different topological indices such as Wiener-type Indices [16], Szeged, vertex PI, first and second Zagreb indices [17], weighted PI index [18], etc. of the corona product of two graphs have already been studied.…”