On regular factors in regular graphs with small radius.
Hoffmann, Arne, Volkmann, Lutz (2004)
The Electronic Journal of Combinatorics [electronic only]
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Hoffmann, Arne, Volkmann, Lutz (2004)
The Electronic Journal of Combinatorics [electronic only]
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Richard M. Davitt, John Frederick Fink, Michael S. Jacobson (1985)
Mathematica Slovaca
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Beezer, Robert A., Farrell, E.J. (2000)
International Journal of Mathematics and Mathematical Sciences
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Dingguo Wang, Erfang Shan (2014)
Discussiones Mathematicae Graph Theory
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A cut-vertex in a graph G is a vertex whose removal increases the number of connected components of G. An end-block of G is a block with a single cut-vertex. In this paper we establish upper bounds on the numbers of end-blocks and cut-vertices in a 4-regular graph G and claw-free 4-regular graphs. We characterize the extremal graphs achieving these bounds.
Polcyn, Joanna (2008)
The Electronic Journal of Combinatorics [electronic only]
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Lepovic, Mirko (2011)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 05C50. We say that a regular graph G of order n and degree r і 1 (which is not the complete graph) is strongly regular if there exist non-negative integers t and q such that |SiЗSj| = t for any two adjacent vertices i and j, and |SiЗSj| = q for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let l1 = r, l2 and l3 be the distinct eigenvalues of a connected strongly regular graph. Let...
Csaba, Béla (2007)
The Electronic Journal of Combinatorics [electronic only]
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Jaroslav Ivančo, Tatiana Polláková (2014)
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.