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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Pavol Híc (1989)
Mathematica Slovaca
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Ferdinand Gliviak (1997)
Mathematica Bohemica
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A graph is called an -graph if its periphery is equal to its center eccentric vertices . Further, a graph is called a -graph if . We describe -graphs and -graphs for small radius. Then, for a given graph and natural numbers , , we construct an -graph of radius having central vertices and containing as an induced subgraph. We prove an analogous existence theorem for -graphs, too. At the end, we give some properties of -graphs and -graphs.
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...
Kumarappan Kathiresan, G. Marimuthu (2010)
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 of the graph and the maximum eccentricity is called the diameter of the graph. The radial graph R(G) based on G has the vertex set as in G, two vertices u and v are adjacent in R(G) if the distance between them in G is equal to the radius of G....
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...