The geodesic transversal problem on some networks

TL;DR

This paper investigates the minimal geodesic transversal sets in specific networks like mesh of trees and chemical structures, providing exact solutions and bounds for these graph invariants.

Contribution

It determines the smallest geodesic transversals in certain interconnection and chemical networks, and establishes general bounds for the invariant.

Findings

Smallest geodesic transversals identified in mesh of trees and silicate networks

Derived bounds for the geodesic transversal invariant

Enhanced understanding of network coverage by geodesic sets

Abstract

A set S of vertices of a graph G is a geodesic transversal of G if every maximal geodesic of G contains at least one vertex of S. We determine a smallest geodesic transversal in certain interconnection networks such as mesh of trees, and some well-known chemical structures such as silicate networks and carbon nanosheets. Some useful general bounds for the corresponding graph invariant are obtained along the way.