论文信息 - Merrifield-Simmons index and minimum Number of Independent Sets in Short Trees

Merrifield-Simmons index and minimum Number of Independent Sets in Short Trees

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 and we give the structure of the extremal trees. A generalization to connected graphs is stated.

Alexander A. Sapozhenko | Preben D. Vestergaard | Anders Sune Pedersen | Allan Frendrup

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