Strong Geodetic Problem in Grid-Like Architectures
نویسندگان
چکیده
منابع مشابه
Strong geodetic problem in grid like architectures
A recent variation of the classical geodetic problem, the strong geodetic problem, is defined as follows. If G is a graph, then sg(G) is the cardinality of a smallest vertex subset S, such that one can assign a fixed geodesic to each pair {x, y} ⊆ S so that these (|S| 2 ) geodesics cover all the vertices of G. In this paper, the strong geodetic problem is studied on Cartesian product graphs. A ...
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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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ژورنال
عنوان ژورنال: Bulletin of the Malaysian Mathematical Sciences Society
سال: 2018
ISSN: 0126-6705,2180-4206
DOI: 10.1007/s40840-018-0609-x