The geodetic domination number of comb product graphs
نویسندگان
چکیده
منابع مشابه
the 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...
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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...
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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 ...
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The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...
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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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ژورنال
عنوان ژورنال: Electronic Journal of Graph Theory and Applications
سال: 2020
ISSN: 2338-2287
DOI: 10.5614/ejgta.2020.8.2.13