Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ |N(ν) ∩ S| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of independent [1, 2]-sets in a family of trees called caterpillars.
Topics
Bioacoustics of insects
REFERENCES
1.
C.
Berge
, The Theory of Graphs and its Applications
, Methuen
, London
, 1962
, pp. 40
–51
.2.
J. A.
Bondy
, and U. S. R.
Murty
, Graph Theory
, Springer
, New York
, 2008
, pp. 1
–30
.3.
M.
Chellali
, O.
Favaron
, T. W.
Haynes
, S. T.
Hedetniemi
, and A.
McRae
, Australas. J. Combin.
59
, 144
–156
(2014
).4.
M.
Chellali
, T. W.
Haynes
, S. T.
Hedetniemi
, and A.
McRae
, Discrete Appl. Math.
161
, 2885
–2893
(2013
).5.
W.
Goddard
and M. A.
Henning
, Discrete Math.
313
, 839
–854
(2013
).6.
T. W.
Haynes
, S. T.
Hedetniemi
, and P. J.
Slater
, Fundamentals of Domination in Graphs
, Marcel Dekker, Inc.
, New York
, 1998
, pp. 1
–71
.7.
C.-H.
Liu
, S.-H
, Poon
, and J.-Y.
Lin
, Theor. Comput. Sci.
562
, 1
–22
(2015
).8.
O.
Ore
, Theory of Graphs
, American Mathematical Society
, Providence, Rhode Island
, 1962
, pp. 206
–223
.9.
X.
Yang
and B.
Wu
, Discrete Appl. Math.
175
, 79
–86
(2014
).10.
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