منابع مشابه
Geodetic number of random graphs of diameter 2
Buckley and Harary introduced several graphical invariants related to convexity theory, such as the geodetic number of a graph. These invariants have been the subject of much study and their determination has been shown to be NP -hard. We use the probabilistic method developed by Erdös to determine the asymptotic behavior of the geodetic number of random graphs with fixed edge probability. As a...
متن کاملDiameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
متن کاملA Generalization of Geodetic Graphs: K{Geodetic Graphs
An undirected graph G = (V;E) is said to be geodetic, if between any pair of vertices x; y 2 V there is a unique shortest path. Generalizations of geodetic graphs are introduced in this paper. K-geodetic graphs are de ned as graphs in which every pair of vertices has at most k paths of minimum length between them. Some properties and characterizations of k{geodetic graphs are studied.
متن کاملOn 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 $k geq 2$, $diam(L(G)) leq k$.
متن کاملGeodetic spectra of graphs
Geodetic numbers of graphs and digraphs have been investigated in the literature recently. The main purpose of this paper is to study the geodetic spectrum of a graph. For any two vertices u and v in an oriented graph D, a u–v geodesic is a shortest directed path from u to v. Let I (u, v) denote the set of all vertices lying on a u–v geodesic. For a vertex subset A, let I (A) denote the union o...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1975
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1975.101300