Displaying similar documents to “Erdős regular graphs of even degree”

Construction of Cospectral Integral Regular Graphs

Ravindra B. Bapat, Masoud Karimi (2017)

Discussiones Mathematicae Graph Theory

Similarity:

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...

Eternal Domination: Criticality and Reachability

William F. Klostermeyer, Gary MacGillivray (2017)

Discussiones Mathematicae Graph Theory

Similarity:

We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs...

Magic and supermagic dense bipartite graphs

Jaroslav Ivanco (2007)

Discussiones Mathematicae Graph Theory

Similarity:

A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.

Ramseyan properties of graphs.

DeLaVina, Ermelinda, Fajtlowicz, Siemion (1996)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

Supermagic Generalized Double Graphs 1

Jaroslav Ivančo (2016)

Discussiones Mathematicae Graph Theory

Similarity:

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.

A characterization of complete tripartite degree-magic graphs

Ľudmila Bezegová, Jaroslav Ivančo (2012)

Discussiones Mathematicae Graph Theory

Similarity:

A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.