Hyperenergetic graphs and cyclomatic number
X. Shen, Y. Hou, I. Gutman, X. Hui (2010)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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X. Shen, Y. Hou, I. Gutman, X. Hui (2010)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Harishchandra S. Ramane, Hanumappa B. Walikar, Siddani Bhaskara Rao, B. Devadas Acharya, Prabhakar R. Hampiholi, Sudhir R. Jog, Ivan Gutman (2004)
Kragujevac Journal of Mathematics
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Snježana Majstorović, Antoaneta Klobučar, Ivan Gutman (2009)
Zbornik Radova
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H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar (2009)
Publications de l'Institut Mathématique
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Petrović, Miroslav (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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Petrović, Miroslav, Milekić, Bojana (2000)
Publications de l'Institut Mathématique. Nouvelle Série
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Ivan Gutman, Bojana Borovićanin (2011)
Zbornik Radova
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Gliviak, Ferdinand, Kyš, P. (1997)
Acta Mathematica Universitatis Comenianae. New Series
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Ying Liu (2013)
Discussiones Mathematicae - General Algebra and Applications
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Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n₊,n₋,n₀) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n₀ denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n - 2ν(G). Guo et al. [Ji-Ming Guo, Weigen Yan and Yeong-Nan Yeh. On the nullity and the matching number...
Bijana Borovićanin, Ivan Gutman (2009)
Zbornik Radova
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Vladislav Bína, Jiří Přibil (2015)
Commentationes Mathematicae Universitatis Carolinae
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The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.