Extremal values of VDB topological indices over catacondensed polyomino systems (2016)
ABSTRACT: A VDB topological index is defined as T = T (G) = X 1≤i≤j≤n−1 mijϕi,j , where G is a graph with n vertices and mij is the number of ij-edges. We study T over the set of catacondensed polyomino systems. Specifically, we introduce two unbranching operations and show that under certain conditions on {ϕij}, T is monotone with respect to these operations. We apply these results to find extremal values of T over the set of catacondensed polyomino systems.