Work

Bounds on the Domination Numbers of δ-Complement Graphs

Year: 2026

Type: article

Abstract: This study examines the δ-complements of graphs—a specific type of graph complement whose adjacency depends on the adjacency of the vertices with identical degrees in the original graph. More specifically, we study this type of complement regarding the domination number. We provide sharp Nordhaus-Gaddum-type bounds on the domination number of a graph and its δ-complement. We also provide sharp bounds on the domination numbers of the δ-complements of joined graphs and Cartesian product graphs.

Source: Mathematics

DOI: 10.3390/math14040734

Authors: Wipawee Tangjai, Chayapa Darayon, Panupong Vichitkunakorn, Rasimate Maungchang, Witsarut Pho-on

Institutions: Mahasarakham University, Dhonburi Rajabhat University, Prince of Songkla University, Walailak University, Srinakharinwirot University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Thailand Science Research and Innovation