Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 10.29252/ijmsi 14 8888 13 en jalali 1386 8 1 gregorian 2007 11 1 2 2 online 1 fulltext
en MORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES عمومى General پژوهشي Research paper <p>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 (n^3) -((9m + 2k)n^2) + 4(m^3) >= 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 .</p> Energy of graph, Spectral graph theory, Biregular graphs, Triregular graphs. 57 62 http://ijmsi.ir/browse.php?a_code=A-10-1-65&slc_lang=en&sid=1 C. Adiga `10031947532846002061` 10031947532846002061 Yes Z. Khoshbakht `10031947532846002062` 10031947532846002062 No I. Gutman `10031947532846002063` 10031947532846002063 No