Geodetic numbers of tensor product and lexicographic product of graphs
Year: 2024
Type: article
Abstract: A shortest u - v path between two vertices u and v of a graph G is a u - v geodesic of G. Let I[u, v] denote the set of all internal vertices lying on some u - v geodesic of G. For a nonempty subset S of V(G), let I(S)=∪u,v∈SI[u,v]. If I(S)=V(G), then S is a geodetic set of G. The cardinality of a minimum geodetic set of G is the geodetic number of G and it is denoted by g(G). In this paper, the exact geodetic numbers of the product graphs T×Km and T°K¯m are obtained, where T is a tree, K¯m denotes the complement of the complete graph Km and, × and ° denote the tensor product and lexicographic product $($also called the wreath product$)$ of graphs, respectively.
Author: K. Raja Chandrasekar
Institution: National Institute of Technology, Puducherry
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,226
OpenAlex ID: W4404230282