Smallest Regular Graphs of Given Degree and Diameter
Martin Knor (2014)
Discussiones Mathematicae Graph Theory
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In this note we present a sharp lower bound on the number of vertices in a regular graph of given degree and diameter.
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Smallest Regular Graphs of Given Degree and Diameter
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Supermagic Graphs Having a Saturated Vertex
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Discussiones Mathematicae Graph Theory
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A graph is called supermagic if it admits a labeling of the edges by pairwise different 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 establish some conditions for graphs with a saturated vertex to be supermagic. Inter alia we show that complete multipartite graphs K1,n,n and K1,2,...,2 are supermagic.