BIREGULAR GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES

Abstract

A graph is said to be biregular if its vertex degrees assume exactly two different values. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Conditions are established under which the inequality E(G) > n is obeyed for connected n-vertex acyclic, unicyclic, and bicyclic biregular graphs.