ScholarWorks@성균관대학교

초록

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: eABC=eABC(Upsilon)=& sum;vivj is an element of E(Upsilon)edi+dj-2didj, where di is the degree of the vertex vi in Upsilon. In this paper, we prove that the double star DSn-3,1 is the second maximal graph with respect to the eABC index of trees of order n. We give an upper bound on eABC of unicyclic graphs of order n and characterize the maximal graphs. The graph K1 boolean OR(P3 boolean OR(n-4)K1) gives the maximal graph with respect to the eABC index of bicyclic graphs of order n. We present several relations between eABC(Upsilon) and ABC(Upsilon) of graph Upsilon. Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research.

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