TY - JOUR

T1 - A simple proof of an inequality connecting the alternating number of independent sets and the decycling number

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

PY - 2011/7/6

Y1 - 2011/7/6

N2 - If sk denotes the number of independent sets of cardinality k and α(G) is the size of a maximum independent set in graph G, then I(G;x)=s0+s1x+⋯+sα( G)xα(G) is the independence polynomial of G (Gutman and Harary, 1983) [8]. In this paper we provide an elementary proof of the inequality|I(G;-1)|≤2φ(G) (Engstrm, 2009) [7], where φ(G) is the decycling number of G (Beineke and Vandell, 1997) [3], namely, the minimum number of vertices that have to be deleted in order to turn G into a forest.

AB - If sk denotes the number of independent sets of cardinality k and α(G) is the size of a maximum independent set in graph G, then I(G;x)=s0+s1x+⋯+sα( G)xα(G) is the independence polynomial of G (Gutman and Harary, 1983) [8]. In this paper we provide an elementary proof of the inequality|I(G;-1)|≤2φ(G) (Engstrm, 2009) [7], where φ(G) is the decycling number of G (Beineke and Vandell, 1997) [3], namely, the minimum number of vertices that have to be deleted in order to turn G into a forest.

KW - Cyclomatic number

KW - Decycling number

KW - Forest

KW - Independence polynomial

KW - Independent set

UR - http://www.scopus.com/inward/record.url?scp=79955474454&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2010.06.004

DO - 10.1016/j.disc.2010.06.004

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AN - SCOPUS:79955474454

SN - 0012-365X

VL - 311

SP - 1204

EP - 1206

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 13

ER -