Chemical Trees with Extermal Sombor Index Among Chemical Trees with Given Order and Number of Vertices of Maximum Degree

Abstract

Gutman and Trinajstic proposed the notion of a degree-based index in 1972. Topological indices based on vertex degree play a signi cant role in graph theory by capturing important structural information about graphs, connectivity and centrality measures, and the identi cation of in uential vertices. These are also valuable in graph classi cation tasks and network modeling, assisting in the categorization of graphs and the comprehension of real-world networks. One of those vertex based topological indices namely Sombor index was introduced by Gutman in 2020. Being a relatively nascent eld, Sombor index has captured the interest of researchers, driving it to become an essential concept in the eld of chemical graph theory. In this work, we nd a chemical tree with maximum Sombor index amoung the class of chemical trees with the xed number of vertices of maximum degree. Similarly, we nd a chemical tree with minimum Sombor index amoung the class of chemical trees with the xed number of vertices of maximum degree.