Bipartite diametrical graphs of diameter 4 and extreme orders.
Al-Addasi, Salah, Al-Ezeh, Hasan (2008)
International Journal of Mathematics and Mathematical Sciences
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Al-Addasi, Salah, Al-Ezeh, Hasan (2008)
International Journal of Mathematics and Mathematical Sciences
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Pavol Híc (1992)
Mathematica Slovaca
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Girse, Robert D. (1986)
International Journal of Mathematics and Mathematical Sciences
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Xu, Xiaodong, Luo, Haipeng, Shao, Zehui (2010)
The Electronic Journal of Combinatorics [electronic only]
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I.B. Lackovic, D.M. Cvetkovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Aneta Dudek, A. Paweł Wojda (2004)
Discussiones Mathematicae Graph Theory
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A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pₘ) of Pₘ-saturated graph of order n. They gave the number sat(n;Pₘ) for n big enough. We deal with similar problem for bipartite graphs.
Robert Fidytek, Hanna Furmańczyk, Paweł Żyliński (2009)
Discussiones Mathematicae Graph Theory
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The Kneser graph K(n,k) is the graph whose vertices correspond to k-element subsets of set {1,2,...,n} and two vertices are adjacent if and only if they represent disjoint subsets. In this paper we study the problem of equitable coloring of Kneser graphs, namely, we establish the equitable chromatic number for graphs K(n,2) and K(n,3). In addition, for sufficiently large n, a tight upper bound on equitable chromatic number of graph K(n,k) is given. Finally, the cases of K(2k,k) and K(2k+1,k)...
Hegde, Suresh Manjanath, Shetty, Sudhakar (2006)
Applied Mathematics E-Notes [electronic only]
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André Bouchet (1999)
Annales de l'institut Fourier
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The following result is proved: if a bipartite graph is not a circle graph, then its complement is not a circle graph. The proof uses Naji’s characterization of circle graphs by means of a linear system of equations with unknowns in . At the end of this short note I briefly recall the work of François Jaeger on circle graphs.
Izak Broere, Johannes Heidema, Peter Mihók (2013)
Discussiones Mathematicae Graph Theory
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Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set [...] of all countable graphs (since every graph in [...] is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of [...] is provided....