The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

Abstract

The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randić index, and the modified-Wiener index among graphs of order n with vertex k-partiteness not more than m .

Discrete Optimization: Theory, Algorithms, and Applications

“…Gao et al [10] consider another graph-theoretic subject, namely they deal with the extremal graphs of some topological indices of a graph G with given vertex k-partiteness, which is defined as the smallest number of vertices, the deletion of which from G yields a k-partite graph. For such graphs, they characterize the extremal values of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like index, the general zeroth-order Randic index, and the modified Wiener index.…”