Domination-related parameters in middle graphs
-
Published:2023-07-12
Issue:
Volume:
Page:
-
ISSN:1793-8309
-
Container-title:Discrete Mathematics, Algorithms and Applications
-
language:en
-
Short-container-title:Discrete Math. Algorithm. Appl.
Affiliation:
1. Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea
Abstract
The middle graph [Formula: see text] of a graph [Formula: see text] is the graph obtained by subdividing each edge of [Formula: see text] exactly once and joining all these newly introduced vertices of adjacent edges of [Formula: see text]. It is known that the decision problems for Italian domination number [Formula: see text], [Formula: see text]-rainbow domination number [Formula: see text] and Roman domination number [Formula: see text] are NP-complete. Recently, it was proved that [Formula: see text] for a graph [Formula: see text] of order [Formula: see text]. In this paper, we continue to study several domination and domatic numbers in middle graphs. We also obtain closed formulas for domination, secure domination and total domination numbers in middle graphs of rooted product graphs.
Funder
National Research Foundation of Korea
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics