Steiner radial number resulting from various graph operations - Gurusamy, R.; Lakshmanan, R.; Ratha Jeyalakshmi, R.; Arockiaraj, S. (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
The Steiner n-radial graph of a graph G on p vertices, denoted by SRn(G), has the vertex set as in G and any n(2 ≤ n ≤ p) vertices are mutually adjacent in SRn(G) if and only if they are n-radial in G. When G is disconnected, any n vertices are mutually adjacent in SRn(G) if not all of them are in the same component. For the edge set of SRn(G), draw Kn corresponding to each set of n-radial vertices. The Steiner radial number rS(G) of a graph G is the least positive integer n such that the Steiner n-radial graph of G is complete. In this paper, Steiner radial number has been determined for the line graph of any tree, total graph of any tree, complement of any tree, sum of two non-trivial trees and Mycielskians of some families. For any pair of positive integers a, b ≥ 3 with a ≤ b, there exists a graph whose Steiner radial number is a and Steiner radial number of its line graph is b.