A note on the graph equation .
Simić, Slobodan K. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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Simić, Slobodan K. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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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.
Filip Guldan (1987)
Časopis pro pěstování matematiky
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Ján Beka (1985)
Mathematica Slovaca
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Anton Kundrík (1990)
Mathematica Slovaca
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Manju K. Menon, A. Vijayakumar (2010)
Discussiones Mathematicae Graph Theory
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The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices,...
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.