- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 71 Issue: 2
- On the well-coveredness of square graphs
On the well-coveredness of square graphs
Authors : Zakir Deniz
Pages : 490-501
Doi:10.31801/cfsuasmas.910947
View : 8 | Download : 5
Publication Date : 2022-06-30
Article Type : Research
Abstract :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 K 1 K1 or K r , r Kr,r for some r ≥ 1 r≥1 . Moreover, we obtain a characterization of the graphs whose squares are well-covered in the case α ( G ) = α ( G 2 ) + k α(G)=α(G2)+k αG=αG2+k α(G)=α(G)2+k for $k\in \{0,1\}$.Keywords : Independent set, distance in graphs, well-covered