On the geodetic iteration number of distance-hereditary graphs
نویسندگان
چکیده
منابع مشابه
Steiner intervals and Steiner geodetic numbers in distance-hereditary graphs
A Steiner tree for a set S of vertices in a connected graph G is a connected subgraph of G with a smallest number of edges that contains S. The Steiner interval I (S) of S is the union of all the vertices of G that belong to some Steiner tree for S. If S = {u, v}, then I (S) = I [u, v] is called the interval between u and v and consists of all vertices that lie on some shortest u–v path in G. T...
متن کاملOn 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 کاملGeodetic and Steiner geodetic sets in 3-Steiner distance hereditary graphs
Let G be a connected graph and S ⊆ V (G). Then the Steiner distance of S, denoted by dG(S), is the smallest number of edges in a connected subgraph of G containing S. Such a subgraph is necessarily a tree called a Steiner tree for S. The Steiner interval for a set S of vertices in a graph, denoted by I (S) is the union of all vertices that belong to some Steiner tree for S. If S = {u, v}, then ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.09.025