Radio number for some thorn graphs

Ruxandra Marinescu-Ghemeci

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 $r (G) = {min}_{u \in V (G)} {e (u)}$ . A graph $G$ is radius-edge-invariant if $r (G - e) = r (G)$ for every $e \in E (G)$ , radius-vertex-invariant if $r (G - v) = r (G)$ for every $v \in V (G)$ and radius-adding-invariant if $r (G + e) = r (G)$ for every $e \in E (\bar{G})$ . 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 $W = {w_{1}, w_{2}, \dots, w_{k}}$ 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 $c_{W} (v) = (d (v, w_{1}), d (v, w_{2}), \dots, d (v, w_{k})) .$ 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 $f V \to {- 1, 0, 1}$ 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 $v \in V$ , $f (N (v)) \geq 1$ , where $N (v)$ consists of every vertex adjacent to $v$ . The weight of an MTDF is $f (V) = \sum f (v)$ , over all vertices $v \in V$ . 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...