Advances and Applications in Discrete Mathematics
Volume 19, Issue 4, Pages 463 - 478
(October 2018) http://dx.doi.org/10.17654/AADMOct2018_463_478 |
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PATH-INDUCED GEODETIC NUMBERS OF THE JOIN AND CORONA OF GRAPHS
Ruthlyn N. Villarante and Imelda S. Aniversario
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Abstract: In [8], a new geodetic parameter was introduced, the path-induced geodetic number of a connected simple graph G which is denoted by Let G be a connected simple nontrivial graph. The distance between two vertices u and v in G, denoted by is the length of a shortest path joining u and v. A shortest u-v path is called a u-v geodesic. For every two vertices u and v of G, the interval denotes all vertices lying in some u-v geodesic. The geodetic closure is the union of intervals between all pairs of vertices from S, that is, A geodetic set of G is a set S with The geodetic number of a graph G is the minimum cardinality of a geodetic set [3].
The researchers find it interesting to study the geodetic set S of G in which the subgraph induced by the set S, denoted by contains a Hamiltonian path P, that is, V(P) = S. Such sets are called path-induced geodetic sets. The concept on path-induced geodetic numbers of graphs can be applied in the problem of saving travel time, facility location, goods distribution, and other distance related concept in graph theory.
The concept of path-induced geodetic numbers of graphs follows from the definition of geodetic numbers of graphs introduced by Buckley and Harary in [2].
In this paper, we investigate the path-induced geodetic sets of a graph G obtained from the join and corona of graphs and determine |
Keywords and phrases: geodetic set, path-induced geodetic set, path-induced geodetic number.
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