Independent sets in chain cacti

Jelena Sedlar

Published 2011-05-10Version 1

In this paper chain cacti are considered. First, for two specific classes of chain cacti (orto-chains and meta-chains of cycles with h vertices) the recurrence relation for independence polynomial is derived. That recurrence relation is then used in deriving explicit expressions for independence number and number of maximum independent sets for such chains. Also, the recurrence relation for total number of independent sets for such graphs is derived. Finaly, the proof is provided that orto-chains and meta-chains are the only extremal chain cacti with respect to total number of independent sets (orto-chains minimal and meta-chains maximal).