منابع مشابه
On the geodetic number of median graphs
A set of vertices S in a graph is called geodetic if every vertex of this graph lies on some shortest path between two vertices from S. In this paper, minimum geodetic sets in median graphs are studied with respect to the operation of peripheral expansion. Along the way geodetic sets of median prisms are considered and median graphs that possess a geodetic set of size two are characterized. © 2...
متن کاملThe geodetic number of strong product graphs
For two vertices u and v of a connected graph G, the set IG[u, v] consists of all those vertices lying on u − v geodesics in G. Given a set S of vertices of G, the union of all sets IG[u, v] for u, v ∈ S is denoted by IG[S]. A set S ⊆ V (G) is a geodetic set if IG[S] = V (G) and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong ...
متن کاملthe geodetic domination number for the product of graphs
a subset $s$ of vertices in a graph $g$ is called a geodetic set if every vertex not in $s$ lies on a shortest path between two vertices from $s$. a subset $d$ of vertices in $g$ is called dominating set if every vertex not in $d$ has at least one neighbor in $d$. a geodetic dominating set $s$ is both a geodetic and a dominating set. the geodetic (domination, geodetic domination) number...
متن کاملMedian graphs , the remoteness function , periphery transversals , and geodetic number two ∗
A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is ...
متن کاملOn the fixed number of graphs
A set of vertices $S$ of a graph $G$ is called a fixing set of $G$, if only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing number of a graph is the smallest cardinality of a fixing set. The fixed number of a graph $G$ is the minimum $k$, such that every $k$-set of vertices of $G$ is a fixing set of $G$. A graph $G$ is called a $k$-fixed graph, if its fix...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.07.119