MORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES

Abstract

The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) >n ,w heren is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a, b ,w ithq quadrangles, if q ≤ abn/ 4a nd 5≤ a<b ≤ (a − 1) 2 /2; (ii) molecular graphs with m edges and k pendent vertices, if 6 n 3 − (9m +2 k)n 2 +4 m 3 ≥ 0; (iii) triregular graphs of degree 1 ,a , b that are quadrangle-free, whose average vertex degree exceeds a ,t hat have not more than 12n/13 pendent vertices, if 5 ≤ a<b ≤ (a − 1) 2 /2.