On-Bond Incident Degree Indices of Square-Hexagonal Chains

For a graph G, its bond incident degree (BID) index is defined as the sum of the contributions fdu,dv over all edges uv of G, where dw denotes the degree of a vertex w of G and f is a real-valued symmetric function. If fdu,dv=du+dv or dudv, then the corresponding BID index is known as the first Zagreb index M1 or the second Zagreb index M2, respectively. The class of square-hexagonal chains is a subclass of the class of molecular graphs of minimum degree 2. (Formal definition of a square-hexagonal chain is given in the Introduction section). The present study is motivated from the paper (C. Xiao, H. Chen, Discrete Math. 339 (2016) 506–510) concerning square-hexagonal chains. In the present paper, a general expression for calculating any BID index of square-hexagonal chains is derived. The chains attaining the maximum or minimum values of M1 and M2 are also characterized from the class of all square-hexagonal chains having a fixed number of polygons.