Work

Mutual-visibility and general position in double graphs and in Mycielskians

Year: 2024

Type: article

Abstract: The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles.

Source: Applied Mathematics and Computation

DOI: 10.1016/j.amc.2024.129131

Authors: Dhanya Roy, Sandi Klavžar, Aparna Lakshmanan S

Institutions: Cochin University of Science and Technology, University of Ljubljana, University of Maribor, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,370

Funders: Cochin University of Science and Technology, Javna Agencija za Raziskovalno Dejavnost RS