Two conjectures on Trinajstic index

Jiajia Wang, Zhen Lin, Min Cai, Shumin Zhang

Abstract


Recently, Furtula introduced a new distance-based topological index named Trinajstic  index, and proposed two conjectures on trees and connected graphs with extremal Trinajstic index. For trees, we solve the conjecture. For connected graphs,we show that the conjecture is true for globular caterpillars.

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