Abstract
The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we introduce a new invariant which is named as F-coindex. Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjunction, symmetric difference of graphs and hence apply our results to find the F-coindex of different chemically interesting molecular graphs and nano-structures.
Highlights
Topological indices are found to be very useful in chemistry, biochemistry and nanotechnology in isomer discrimination, structure–property relationship, structure-activity relationship and pharmaceutical drug design
Like Zagreb coindices, corresponding to F-index, we introduce here a new invariant, the F-coindex which is defined as follows
We find the correlation between the logarithm of the octanol-water partition coefficient (P) and the corresponding F-coindex values of octane isomers
Summary
Topological indices are found to be very useful in chemistry, biochemistry and nanotechnology in isomer discrimination, structure–property relationship, structure-activity relationship and pharmaceutical drug design. Let G be a simple connected graph with vertex set V(G) and edge set E(G) respectively. Let, for any vertex v ∈ V (G), dG(v) denotes its degree, that is the number of adjacent vertices of v in G. The complement of a graph G is denoted by Gand is the simple graph with the same vertex set V(G). Any two vertices uv ∈ E(G ) if and only if uv ∈/ E(G).
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