The square of a graph G is obtained from G by putting an edge between two distinct vertices whenever their distance in G is 2. A graph is well-covered if every maximal independent set in the graph is of the same size. In this paper, we investigate the graphs whose squares are well-covered. We first provide a characterization of the trees whose squares are well-covered. Afterwards, we show that a bipartite graph G and its square are well-covered if and only if every component of G is K1K1 or Kr,rKr,r for some r≥1r≥1. Moreover, we obtain a characterization of the graphs whose squares are well-covered in the case α(G)=α(G2)+kα(G)=α(G2)+kαG=αG2+k
α(G)=α(G)2+k for $k\in \{0,1\}$.
The Scientific and Technological Research Council of Turkey
121F018
121F018
Birincil Dil | İngilizce |
---|---|
Konular | Uygulamalı Matematik |
Bölüm | Research Article |
Yazarlar | |
Proje Numarası | 121F018 |
Yayımlanma Tarihi | 30 Haziran 2022 |
Gönderilme Tarihi | 30 Nisan 2021 |
Kabul Tarihi | 13 Ocak 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 71 Sayı: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.