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Total eccentricity, adjacent eccentric distance sum and gutman index of certain special molecular graphs

Wei Gao, Li Liang, Yun Gao

Chemical compounds and drugs are often modeled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, we determine the total eccentricity, adjacent eccentric distance sum and Gutman index of fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs.