Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. In this paper, we propose a definition of generalized bridge molecular graphs that can model more kinds of long chain polymerization products than the bridge molecular graphs, and provide some results of the edge versions of atom-bond connectivity ( A B C e ) and geometric arithmetic ( G A e ) indices for some generalized bridge molecular graphs, which have regular, periodic and symmetrical structures. The results of this paper offer promising prospects in the applications for chemical and material engineering, especially in chemical industry research.
The general sum-connectivity index χ α (G), for a (molecular) graph G, is defined as the sum of the weightsdenotes the degree of a vertex a 1 (or a 2 ) in the graph G; E(G) denotes the set of edges of G, and α is an arbitrary real number. Eliasi and Taeri (Discrete Appl. Math.
The general sum-connectivity index is a molecular descriptor defined as , where denotes the degree of a vertex , and α is a real number. Let X be a graph; then let be the graph obtained from X by adding a new vertex corresponding to each edge of X and joining to the end vertices of the corresponding edge . In this paper we obtain the lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph. Additionally, we determine the bounds for the general sum-connectivity index of line graph and rooted product of graphs.
The degree-based topological indices correlate certain physicochemical properties such as boiling point, strain energy, and stability, etc., of certain chemical compounds. Among the major classes of topological indices are the distance-based topological indices, degree-based topological indices, and counting-related polynomials and corresponding indices of graphs. Among all of the degree-based indices, namely the first general Zagreb index, general Rndić connectivity index, general sum-connectivity index, atom–bond connectivity index (ABC), and geometric–arithmetic index (GA), are most important due to their chemical significance. In this paper, we compute the first general Zagreb index, general Randić connectivity index, general sum-connectivity index, ABC, GA, ABC4, and GA5 indices of hexagonal parallelogram P(m,n) nanotubes, triangular benzenoid Gn, and zigzag-edge coronoid fused with starphene ZCS(k,l,m) nanotubes by using the line graphs of the subdivision of these chemical graphs.
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