A generalization of the friendship theorem
Marián Sudolský (1978)
Mathematica Slovaca
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Marián Sudolský (1978)
Mathematica Slovaca
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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...
Wong, P.K. (1985)
International Journal of Mathematics and Mathematical Sciences
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Ferdinand Gliviak, Peter Kyš, Ján Plesník (1969)
Matematický časopis
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Vladimir Samodivkin (2008)
Discussiones Mathematicae Graph Theory
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The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of a graph G with |D| = γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-good if x belongs to some γ-set and (ii) γ-bad if x belongs to no γ-set. The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph...
Bollobás, Béla, Nikiforov, Vladimir (2005)
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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K.M. Kathiresan, G. Marimuthu, C. Parameswaran (2014)
Discussiones Mathematicae Graph Theory
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In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R*(G) based on G has the vertex set as in G and two vertices u and v are adjacent in R*(G) if the distance between them in G is...
Exoo, Geoffrey (2002)
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.