Displaying similar documents to “On Γ-regular graphs”

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).

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...

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.