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Radio number for some thorn graphs

100%

Marinescu-Ghemeci R.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 2

201-222

For a graph G and any two vertices u and v in G, let d(u,v) denote the distance between u and v and let diam(G) be the diameter of G. A multilevel distance labeling (or radio labeling) for G is a function f that assigns to each vertex of G a positive integer such that for any two distinct vertices u and v, d(u,v) + |f(u) - f(v)| ≥ diam(G) + 1. The largest integer in the range of f is called the span of f and is denoted span(f). The radio number of G, denoted rn(G), is the minimum span of any radio labeling for G. A thorn graph is a graph obtained from a given graph by attaching new terminal vertices to the vertices of the initial graph. In this paper the radio numbers for two classes of thorn graphs are determined: the caterpillar obtained from the path Pₙ by attaching a new terminal vertex to each non-terminal vertex and the thorn star $S_{n,k}$ obtained from the star Sₙ by attaching k new terminal vertices to each terminal vertex of the star.

On the packing of two copies of a caterpillar in its third power

88%

Germain C., Kheddouci H.

Discussiones Mathematicae Graph Theory

2003

tom 23

nr 1

105-115

H. Kheddouci, J.F. Saclé and M. Woźniak conjectured in 2000 that if a tree T is not a star, then there is an edge-disjoint placement of T into its third power.In this paper, we prove the conjecture for caterpillars.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Germain C.

1 Kheddouci H.

1 Marinescu-Ghemeci R.

1 2010

1 2003

Wyniki wyszukiwania

Radio number for some thorn graphs

On the packing of two copies of a caterpillar in its third power