Work

Complete forcing numbers of the Rook’s graphs

Year: 2025

Type: article

Abstract: A subset of the edges of a perfect matching in a graph is called a forcing set for it if no other perfect matching contains that subset. A complete forcing set of a graph is a subset of the edges such that the intersection of every perfect matching with the subset forms a forcing set for that perfect matching. The minimum size of the complete forcing sets of a graph is called the complete forcing number of the graph. In this paper, we determine the complete forcing number of the Cartesian product of two complete graphs, also known as Rook’s graphs, and present a minimum-sized complete forcing set for these graphs. For higher-dimensional Cartesian products of complete graphs, we use the result of the 2-fold Cartesian product case to present upper and lower bounds for the complete forcing number.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2025.10.031

Authors: Javad Ebrahimi Boroojeni, Aref Namayandeh

Institution: Sharif University of Technology

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Instituto Politécnico de Macau, School of Mathematics, Institute for Research in Fundamental Sciences, Institute for Research in Fundamental Sciences