On strict-double-bound graphs and Cartesian products of paths and cycles-Reference-Cited by-同舟云学术

On strict-double-bound graphs and Cartesian products of paths and cycles

Published:2023-07-17 Issue: Volume: Page:
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Egawa Yoshimi¹,Ogawa Kenjiro²^ORCID,Ozeki Kenta³,Tagusari Satoshi²,Tsuchiya Morimasa²

Affiliation:

1. Department of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

2. Department of Mathematical Sciences, Tokai University, Hiratsuka 259-1292, Japan

3. Faculty of Environment and Information Sciences, Yokohama National University, 79-2 Tokiwadai Hodogaya-ku, Yokohama 240-8501, Japan

Abstract

For a poset [Formula: see text] the strict-double-bound graph ([Formula: see text]) of [Formula: see text] is the graph with the vertex set [Formula: see text] such that [Formula: see text] if and only if [Formula: see text] and there exist [Formula: see text] and [Formula: see text] distinct from [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text] For a connected graph [Formula: see text], the strict-double-bound number [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the graph with [Formula: see text] vertices and no edges. In this paper we deal with the strict-double-bound numbers of Cartesian products of graphs. We show that [Formula: see text] for [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text] for [Formula: see text].

Publisher

World Scientific Pub Co Pte Ltd

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830923500581