TY - RPRT
T1 - Merrifield-Simmons index and minimum number of independent sets in shor trees
AU - Frendrup, Allan
AU - Pedersen, Anders Sune
AU - Sapozhenko, Alexander A.
AU - Vestergaard, Preben D.
PY - 2009
Y1 - 2009
N2 - In Ars Comb. 84 (2007), 85-96, Pedersen and Vestergaard posed the problem of determining a lower bound for the number of independent sets in a tree of fixed order and diameter d. Asymptotically, we give here a complete solution for trees of diameter d ≤ 5. The lower bound is 5 n/3 and we give the structure of the extremal trees. A generalization to connected graphs is stated.
AB - In Ars Comb. 84 (2007), 85-96, Pedersen and Vestergaard posed the problem of determining a lower bound for the number of independent sets in a tree of fixed order and diameter d. Asymptotically, we give here a complete solution for trees of diameter d ≤ 5. The lower bound is 5 n/3 and we give the structure of the extremal trees. A generalization to connected graphs is stated.
M3 - Report
T3 - Research Report Series
BT - Merrifield-Simmons index and minimum number of independent sets in shor trees
PB - Department of Mathematical Sciences, Aalborg University
CY - Aalborg
ER -