On the Extension of Graphs with a Given Diameter without Superfluous Edges
Ferdinand Gliviak, Peter Kyš, Ján Plesník (1969)
Matematický časopis
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Ferdinand Gliviak, Peter Kyš, Ján Plesník (1969)
Matematický časopis
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Girse, Robert D. (1986)
International Journal of Mathematics and Mathematical Sciences
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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...
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.
Jeongmi Park, Yoshio Sano (2014)
Discussiones Mathematicae Graph Theory
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The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N+D(x) ∩ N+D(y) ≠ ∅ or N−D(x) ∩ N−D(y) ≠ ∅, where N+D(x) (resp. N−D(x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order ) if there exist a real-valued function f : V → R on the set V and a positive real number δ ∈ R such that (x, y) ∈ A if...
Peter Bugata, Mirko Horňák, Stanislav Jendroľ (1989)
Časopis pro pěstování matematiky
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Walter Carballosa, Ruy Fabila-Monroy, Jesús Leaños, Luis Manuel Rivera (2017)
Discussiones Mathematicae Graph Theory
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Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this paper we characterize precisely, for each value of k, which graphs have a regular k-token graph and which connected graphs have a planar k-token graph.