A Unified Approach to Extremal Cacti for Different Indices
نویسندگان
چکیده
Abstract Many chemical indices have been invented in theoretical chemistry, such as Wiener index, Merrifield-Simmons index, Hosoya index, spectral radius and Randić index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) the set of cacti of order n and with r cycles. Obviously, G (n, 0) is the set of all trees and G (n, 1) is the set of all unicyclic graphs. In this paper, we present a unified approach to the extremal cactus, which have the same or very similar structures, for Wiener index, Merrifield-Simmons index, Hosoya index and spectral radius. From our results, we can derive some known results.
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