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Studies of polyphenylene graphs using connection number based zagreb indices.
(UMT Lahore, 2022) Abdur Razzaq
The field of graph theory plays an important role in cheminformatics, especially in mathematics and chemistry, to develop several chemical structures with the help of numerical parameters (topological indices). A topological index (TI) is a function from the set of graphs to the set of real numbers that associates a real number to each molecular graph. Moreover, for two graphs K1 and K2, if K1 = K2 then TI (K1) = TI(K2). The first topological index was introduced by Wiener (1947). Gutman and Trinajastic (1972) introduced degree and connection based TIs. The degree and connection number of a vertex v in K is the number of vertices at distance 1 and 2 respectively, from v in K. In this paper, we computed several connection based Zagreb indices such as first Zagreb connection index, second Zagreb connection index, modified first Zagreb connection index, modified second Zagreb connection index, modified third Zagreb connection index, modified fourth Zagreb connection index, first multiplicative Zagreb connection index, second multiplicative Zagreb connection index, third multiplicative Zagreb connection index, fourth multiplicative Zagreb connection index, modified first multiplicative Zagreb connection index, modified second multiplicative Zagreb connection index, modified third multiplicative Zagreb connection index for Polyphenylene graph.