Unified extremal results of topological indices and spectral invariants of graphs

Abstract

Identifying graphs with extremal properties is an extensively studied topic in both topological graph theory and spectral graph theory. As observed in the literature, for many graph categories the extremal graphs with respect to some prescribed topological index or spectral invariant are the same. Therefore, it is an interesting problem to find a unified method to identify the extremal graphs for a set of topological or spectral invariants. Here we consider the majorization theorem to obtain extremal graphs in the class of trees, unicyclic graphs and bicyclic graphs with given order and fixed maximum degree, independence number, matching number, domination number, and/or number of pendant vertices, respectively.