SOME BOUNDS FOR THE WIENER INDEX OF WEAK JOIN OF TWO GRAPHS

Abstract

In 2020, G. Suresh Singh and Manju V. N. \cite{mvn} introduced the concept of weak join of two disjoint graphs with respect to the degrees of the given graphs and categorized them as homogeneous weak join, heterogeneous weak join and studied some of their properties. Homogeneous weak join can be splitted in to three cases namely, odd to odd degree weak join, even to even degree weak join, odd to odd and even to even degree weak join. Similarly, heterogeneous weak join includes the other three cases namely, odd to even degree weak join, even to odd degree weak join, odd to even and even to odd degree weak join. In this paper we try to find bounds for the Wiener index of odd to odd, even to even, odd to even and even to odd degree weak join of graphs.