کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6416889 1336897 2011 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Complete solution to a problem on the maximal energy of unicyclic bipartite graphs
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Complete solution to a problem on the maximal energy of unicyclic bipartite graphs
چکیده انگلیسی

The energy of a simple graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Denote by Cn the cycle, and Pn6 the unicyclic graph obtained by connecting a vertex of C6 with a leaf of Pn-6. Caporossi et al. conjectured that the unicyclic graph with maximal energy is Pn6 for n=8,12,14 and n≥16. In Hou et al. (2002) [Y. Hou, I. Gutman, C. Woo, Unicyclic graphs with maximal energy, Linear Algebra Appl. 356 (2002) 27-36], the authors proved that E(Pn6) is maximal within the class of the unicyclic bipartite n-vertex graphs differing from Cn. And they also claimed that the energies of Cn and Pn6 is quasi-order incomparable and left this as an open problem. In this paper, by utilizing the Coulson integral formula and some knowledge of real analysis, especially by employing certain combinatorial techniques, we show that the energy of Pn6 is greater than that of Cn for n=8,12,14 and n≥16, which completely solves this open problem and partially solves the above conjecture.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 434, Issue 5, 1 March 2011, Pages 1370-1377
نویسندگان
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