MORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES

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 , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a; b , with q quadrangles, if q  abn=4 and 5  a < b  (a ?? 1)2=2 ; (ii) molecular graphs with m edges and k pendent vertices, if 6 n3 ?? (9m + 2k)n2 + 4m3  0 ; (iii) triregular graphs of degree 1; a; b that are quadrangle{free, whose average vertex degree exceeds a , that have not more than 12n=13 pendent vertices, if 5  a < b  (a ?? 1)2=2 .