Displaying similar documents to “Integral Cayley graphs over Abelian groups.”

Note on group distance magic complete bipartite graphs

Sylwia Cichacz (2014)

Open Mathematics

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A Γ-distance magic labeling of a graph G = (V, E) with |V| = n is a bijection ℓ from V to an Abelian group Γ of order n such that the weight w ( x ) = y N G ( x ) ( y ) of every vertex x ∈ V is equal to the same element µ ∈ Γ, called the magic constant. A graph G is called a group distance magic graph if there exists a Γ-distance magic labeling for every Abelian group Γ of order |V(G)|. In this paper we give necessary and sufficient conditions for complete k-partite graphs of odd order p to be ℤp-distance magic....

Bounding neighbor-connectivity of Abelian Cayley graphs

Lynne L. Doty (2011)

Discussiones Mathematicae Graph Theory

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For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. Doty has sharpened that bound in abelian Cayley graphs to approximately...

Integral Cayley Sum Graphs and Groups

Xuanlong Ma, Kaishun Wang (2016)

Discussiones Mathematicae Graph Theory

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For any positive integer k, let Ak denote the set of finite abelian groups G such that for any subgroup H of G all Cayley sum graphs CayS(H, S) are integral if |S| = k. A finite abelian group G is called Cayley sum integral if for any subgroup H of G all Cayley sum graphs on H are integral. In this paper, the classes A2 and A3 are classified. As an application, we determine all finite Cayley sum integral groups.

Dynamic cage survey.

Exoo, Geoffrey, Jajcay, Robert (2008)

The Electronic Journal of Combinatorics [electronic only]

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