On the well-coveredness of square graphs
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
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
or
K
r
,
r
for some
r
≥
1
. Moreover, we obtain a characterization of the graphs whose squares are well-covered in the case
α
(
G
)
=
α
(
G
2
)
+
k
for
k
∈
{
0
,
1
}
.
Description
Keywords
Independent set, distance in graphs, well-covered