Displaying similar documents to “The join of split graphs whose completely regular endomorphisms form a monoid”

Construction of Cospectral Integral Regular Graphs

Ravindra B. Bapat, Masoud Karimi (2017)

Discussiones Mathematicae Graph Theory

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Graphs G and H are called cospectral if they have the same characteristic polynomial. If eigenvalues are integral, then corresponding graphs are called integral graph. In this article we introduce a construction to produce pairs of cospectral integral regular graphs. Generalizing the construction of G4(a, b) and G5(a, b) due to Wang and Sun, we define graphs 𝒢4(G,H) and 𝒢5(G,H) and show that they are cospectral integral regular when G is an integral q-regular graph of order m and H...

Metrically regular square of metrically regular bigraphs. II.

Vladimír Vetchý (1992)

Archivum Mathematicum

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Metrically regular bigraphs the square of which are metrically regular graphs are investigated in the case of graphs with 6 distinct eigenvalues (these eigenvalues can have variuos multiplicities).

Erdős regular graphs of even degree

Andrey A. Dobrynin, Leonid S. Mel'nikov, Artem V. Pyatkin (2007)

Discussiones Mathematicae Graph Theory

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In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. In 1989, Erdös conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6,7]. Results of a computer search for graphs of degree r = 12,14,16 are presented. All the graphs found are both r-regular and r-connected.

Supermagic Generalized Double Graphs 1

Jaroslav Ivančo (2016)

Discussiones Mathematicae Graph Theory

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A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.