نتایج جستجو برای: geodetic domination number
تعداد نتایج: 1177024 فیلتر نتایج به سال:
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...
In this paper, we study both concepts of geodetic dominatingand edge geodetic dominating sets and derive some tight upper bounds onthe edge geodetic and the edge geodetic domination numbers. We also obtainattainable upper bounds on the maximum number of elements in a partitionof a vertex set of a connected graph into geodetic sets, edge geodetic sets,geodetic domin...
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 g(G)(γ(G), γg(G)) of G is...
let g=(v,e) be a graph with vertex set v and edge set e.for two vertices u,v of g ,the closed interval i[u,v] ,consists of u,v and all vertices lying in some u-v geodesic in g.if s is a set of vertices of g then i[s]is the union of all sets i[u,v]for u,v ? s. if i[s]=v(g) , then s is a geodetic set for g.the geodetic number g(g) is the minimum cardinality of geodetic set.the maximum cardinalit...
In this paper, we introduce a new graph theoretic parameter, split edge geodetic domination number of connected as follows. A set S ⊆ V(G) is said to be dominating G if both and ( < V-S > disconnected). The minimum cardinality the called denoted by γ1gs(G). It shown that for any 3 positive integers m, f nwith 2 ≤ m n-2, there exists order n such g1 (G) = γ1gs f. For every pair l, with l γ1gs(G)...
Let G be a connected graph. For two vertices u and v in G, a u–v geodesic is any shortest path joining u and v. The closed geodetic interval IG[u, v] consists of all vertices of G lying on any u–v geodesic. For S ⊆ V (G), S is a geodetic set in G if ⋃ u,v∈S IG[u, v] = V (G). Vertices u and v of G are neighbors if u and v are adjacent. The closed neighborhood NG[v] of vertex v consists of v and ...
A subset S of vertices in a graph G is a called a geodetic dominating set if S is both a geodetic set and a (standard) dominating set. In this paper, we study geodetic domination on graphs.
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