ScholarWorks@성균관대학교

초록

In graph theory and molecular modeling, the search for effective and computationally efficient graph invariants has driven the exploration of various topological indices. Among them, the multiplicative Sombor index has gained considerable attention for its solid mathematical foundations and impressive discriminative ability. Let G=(V,E) be a graph of order n . The multiplicative version of the Sombor index of a graph was developed very recently. The multiplicative Sombor index is defined as ΠSO=ΠSO(G)=∏vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the degree of the vertex vi in G . In this paper, we establish that the double star DSn−3,1 is the second maximal tree concerning the multiplicative Sombor index among trees of order n . We also derive both lower and upper bounds on the multiplicative Sombor index for unicyclic graphs of order n and identify the extremal graphs. Additionally, we determine the minimal graphs with respect to the multiplicative Sombor index of quasi-trees. Furthermore, we provide an upper bound on the multiplicative Sombor index for graphs of order n with vertex connectivity k , and characterize the extremal graphs. Finally, we conclude the paper and outline directions for future research.

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