Displaying similar documents to “Radio number for some thorn graphs”

Radius-invariant graphs

Vojtech Bálint, Ondrej Vacek (2004)

Mathematica Bohemica

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The eccentricity e ( v ) of a vertex v is defined as the distance to a farthest vertex from v . The radius of a graph G is defined as a r ( G ) = min u V ( G ) { e ( u ) } . A graph G is radius-edge-invariant if r ( G - e ) = r ( G ) for every e E ( G ) , radius-vertex-invariant if r ( G - v ) = r ( G ) for every v V ( G ) and radius-adding-invariant if r ( G + e ) = r ( G ) for every e E ( G ¯ ) . Such classes of graphs are studied in this paper.

Vertex-disjoint stars in graphs

Katsuhiro Ota (2001)

Discussiones Mathematicae Graph Theory

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In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t-1 and the order is at least (t+1)k + O(t²), then the graph contains k vertex-disjoint copies of a star K 1 , t . The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.

The independent resolving number of a graph

Gary Chartrand, Varaporn Saenpholphat, Ping Zhang (2003)

Mathematica Bohemica

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For an ordered set W = { w 1 , w 2 , , w k } of vertices in a connected graph G and a vertex v of G , the code of v with respect to W is the k -vector c W ( v ) = ( d ( v , w 1 ) , d ( v , w 2 ) , , d ( v , w k ) ) . The set W is an independent resolving set for G if (1) W is independent in G and (2) distinct vertices have distinct codes with respect to W . The cardinality of a minimum independent resolving set in G is the independent resolving number i r ( G ) . We study the existence of independent resolving sets in graphs, characterize all nontrivial connected graphs G of order...

Minus total domination in graphs

Hua Ming Xing, Hai-Long Liu (2009)

Czechoslovak Mathematical Journal

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A three-valued function f V { - 1 , 0 , 1 } defined on the vertices of a graph G = ( V , E ) is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every v V , f ( N ( v ) ) 1 , where N ( v ) consists of every vertex adjacent to v . The weight of an MTDF is f ( V ) = f ( v ) , over all vertices v V . The minus total domination number of a graph G , denoted γ t - ( G ) , equals the minimum weight of an MTDF of G . In this paper, we discuss some properties of minus total domination on a graph...

Bounds concerning the alliance number

Grady Bullington, Linda Eroh, Steven J. Winters (2009)

Mathematica Bohemica

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P. Kristiansen, S. M. Hedetniemi, and S. T. Hedetniemi, in Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004), 157–177, and T. W. Haynes, S. T. Hedetniemi, and M. A. Henning, in Global defensive alliances in graphs, Electron. J. Combin. 10 (2003), introduced the defensive alliance number a ( G ) , strong defensive alliance number a ^ ( G ) , and global defensive alliance number γ a ( G ) . In this paper, we consider relationships between these parameters and the domination number γ ( G ) . For any positive...