Computing Certain Topological Indices of Indu-Bala Product of Graphs

Abstract

The Indu-Bala product G₁▼G₂ of graphs G₁ and G₂ is obtained from two disjoint copies of the join G₁ ∨ G₂ of G₁ and G₂ by joining the corresponding vertices in the two copies of G₂. In this paper we obtain the explicit formulae for certain degree and distance based topological indices viz. first Zagreb index, second Zagreb index, third Zagreb index, F-index, hyper-Zagreb index, harmonic index, first multiplicative Zagreb index, second multiplicative Zagreb index, modified first multiplicative Zagreb index, Wiener index, Harary index, sum-degree distance index, product-degree distance index, reciprocal sum-degree distance index and reciprocal product-degree distance index of Indu-Bala product of graphs. Also, we present the exact value of the distance based topological indices of graph
G in terms of its order, size and Zagreb indices, when diam(G) ≤ 2.

Key words and phrases. Degree, distance, topological indices, Indu-Bala product of graphs.

2020 Mathematics Subject Classification. 05C09