An O(mn^2) algorithm for computing the strong geodetic number in outerplanar graphs
نویسندگان
چکیده
منابع مشابه
The 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 ...
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For n-vertex outerplanar graphs, it is proven that O(n) is an upper bound on the number of breakpoints of the function which gives the maximum weight of an independent set, where the vertex weights vary as linear functions of a parameter. An O(n) algorithm for finding the solution is proposed.
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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...
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For a graph G, let τ(G) be the decycling number of G and c(G) be the number of vertex-disjoint cycles of G. It has been proved that c(G)≤ τ(G)≤ 2c(G) for an outerplanar graph G. An outerplanar graph G is called lower-extremal if τ(G)= c(G) and upper-extremal if τ(G)= 2c(G). In this paper, we provide a necessary and sufficient condition for an outerplanar graph being upper-extremal. On the other...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2020
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2311