Discussing graph theory with a computer. II: Theorems suggested by the computer.
Cvetkovic, Dragos M. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
Cvetkovic, Dragos M. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
Petrović, Miroslav (1991)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar (2009)
Publications de l'Institut Mathématique
Similarity:
D. M. Cardoso, D. Cvetković (2006)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Similarity:
Vladislav Bína, Jiří Přibil (2015)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
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.
Jianfeng Wang, Haixing Zhao, Qiongxiang Huang (2012)
Czechoslovak Mathematical Journal
Similarity:
A multicone graph is defined to be the join of a clique and a regular graph. Based on Zhou and Cho's result [B. Zhou, H. H. Cho, Remarks on spectral radius and Laplacian eigenvalues of a graph, Czech. Math. J. 55 (130) (2005), 781–790], the spectral characterization of multicone graphs is investigated. Particularly, we determine a necessary and sufficient condition for two multicone graphs to be cospectral graphs and investigate the structures of graphs cospectral to a multicone graph....
Torgašev, Aleksandar (1992)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
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
Similarity:
I.B. Lackovic, D.M. Cvetkovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
Similarity:
Ľubomír Šoltés (1992)
Mathematica Slovaca
Similarity:
Daniel C. Slilaty, Thomas Zaslavsky (2015)
Discussiones Mathematicae Graph Theory
Similarity:
The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does...
Peter Hudák, Mária Maceková, Tomáš Madaras, Pavol Široczki (2016)
Discussiones Mathematicae Graph Theory
Similarity:
A graph H is defined to be light in a graph family 𝒢 if there exist finite numbers φ(H, 𝒢) and w(H, 𝒢) such that each G ∈ 𝒢 which contains H as a subgraph, also contains its isomorphic copy K with ΔG(K) ≤ φ(H, 𝒢) and ∑x∈V(K) degG(x) ≤ w(H, 𝒢). In this paper, we investigate light graphs in families of plane graphs of minimum degree 2 with prescribed girth and no adjacent 2-vertices, specifying several necessary conditions for their lightness and providing sharp bounds on φ and w...
Walter Carballosa, Ruy Fabila-Monroy, Jesús Leaños, Luis Manuel Rivera (2017)
Discussiones Mathematicae Graph Theory
Similarity:
Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this paper we characterize precisely, for each value of k, which graphs have a regular k-token graph and which connected graphs have a planar k-token graph.