منابع مشابه
On Diameter of Line Graphs
The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
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A ranking of a graph is a coloring of the vertex set with positive integers such that on every path connecting two vertices of the same color there is a vertex of larger color. We consider the directed variant of this problem, where the above condition is imposed only on those paths in which all edges are oriented in the same direction. We show that the ranking number of a directed tree is boun...
متن کاملRankings of Graphs
A vertex (edge) coloring φ : V → {1, 2, . . . , t} (φ′ : E → {1, 2, . . . , t}) of a graph G = (V,E) is a vertex (edge) t-ranking if, for any two vertices (edges) of the same color, every path between them contains a vertex (edge) of larger color. The vertex ranking number χr(G) (edge ranking number χ′ r (G)) is the smallest value of t such that G has a vertex (edge) t-ranking. In this paper we...
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A vertex ranking of a graph is an assignment of ranks (or colors) to the vertices of the graph, in such a way that any simple path connecting two vertices of equal rank, must contain a vertex of a higher rank. In this paper we study a relaxation of this notion, in which the requirement above should only hold for paths of some bounded length l for some fixed l. For instance, already the case l =...
متن کاملMinimal k-rankings for prism graphs
We determine rank numbers for the prism graph P 2 ×C n (P 2 being the connected two-node graph and C n a cycle of length n) and for the square of an even cycle.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00215-0