Frendrup, Allan

Pedersen, Anders Sune

Sapozhenko, Alexander A.

Vestergaard, Preben D.

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.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

Merrifield-Simmons index and minimum number of independent sets in shor trees

http://vbn.aau.dk/files/16533041/R-2009-03.pdf

Merrifield-Simmons index and minimum number of independent sets in shor trees

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