TY - JOUR
T1 - Graph Operations Preserving W2-Property
AU - Levit, Vadim E.
AU - Mandrescu, Eugen
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/7
Y1 - 2018/7
N2 - A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class Wn if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W1 is the family of all well-covered graphs. Staples showed a number of ways to build graphs in Wn, using graphs from Wn or Wn+1. In this paper, we construct some more infinite subfamilies of the class W2 by means of corona, join, and rooted product of graphs.
AB - A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class Wn if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W1 is the family of all well-covered graphs. Staples showed a number of ways to build graphs in Wn, using graphs from Wn or Wn+1. In this paper, we construct some more infinite subfamilies of the class W2 by means of corona, join, and rooted product of graphs.
KW - class W
KW - corona of graphs
KW - graph join
KW - independent set
KW - rooted product of graphs
KW - shedding vertex
KW - well-covered graph
UR - http://www.scopus.com/inward/record.url?scp=85049905074&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2018.06.007
DO - 10.1016/j.endm.2018.06.007
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AN - SCOPUS:85049905074
SN - 1571-0653
VL - 68
SP - 35
EP - 40
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -