### The number of edges on generalizations of Paley graphs.

Sze, Lawrence (2001)

International Journal of Mathematics and Mathematical Sciences

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Sze, Lawrence (2001)

International Journal of Mathematics and Mathematical Sciences

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Lidia Badura (2014)

Discussiones Mathematicae Graph Theory

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Let G = G1 ∪ G2 be the sum of two simple graphs G1,G2 having a common edge or G = G1 ∪ e1 ∪ e2 ∪ G2 be the sum of two simple disjoint graphs G1,G2 connected by two edges e1 and e2 which form a cycle C4 inside G. We give a method of computing the determinant det A(G) of the adjacency matrix of G by reducing the calculation of the determinant to certain subgraphs of G1 and G2. To show the scope and effectiveness of our method we give some examples

Jaroslav Ivančo, Z. Lastivková, A. Semaničová (2004)

Mathematica Bohemica

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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. We characterize magic line graphs of general graphs and describe some class of supermagic line graphs of bipartite graphs.

Milan Koman (1970)

Matematický časopis

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Stanislav Jendroľ, Vladimír Žoldák (1995)

Mathematica Slovaca

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Nathanson, Melvyn B., Sullivan, Blair D. (2008)

Integers

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Jaroslav Ivančo (2000)

Mathematica Bohemica

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A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. Some constructions of supermagic labellings of regular graphs are described. Supermagic regular complete multipartite graphs and supermagic cubes are characterized.