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Regular plane tessellations can easily be constructed by repeating regular polygons. This design is of extreme importance for direct interconnection networks as it yields high overall performance. The honeycomb and the hexagonal networks are two such popular mesh-derived parallel networks. The first and second Zagreb indices are among the most studied topological indices. We now consider analogous graph invariants, based on the second degrees of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for the Hex, Hex derived and some honeycomb networks. [ABSTRACT FROM AUTHOR]

Graph theory has made much advancement in the field of mathematical chemistry in last few decades. Now a days, chemical graph theory has become very popular among researchers because of its wide range of applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields. In this article, we study the chemical graph of honeycomb network denoted by HCn and compute the total eccentricity index, average eccentricity index, eccentricity based Zagreb indices, atom-bond connectivity index and geometricarithmetic index of honeycomb networks. Furthermore, we give analytically closed formulas of these indices which are helpful in studying the underlying topologies of this netwrok. [ABSTRACT FROM AUTHOR]