The F-coindex of some graph operations

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.

F-index of graphs based on four operations related to the lexicographic product

“…Furtula et al,in [5], investigate some basic properties and bounds of F-index and in [6] Abdoa et al found the extremal trees with respect to the F-index. Recently, the present author studied this index for different graph operations [7] and of different classes of nanostar dendrimers [9] and also introduced F-coindex in [8]. Also, the present author studied F-index of different transformation graphs and four sum of graphs in [10] and [11] respectively.…”

Bounds on F-index of tricyclic graphs with fixed pendant vertices

“…They also proposed its basic properties in the same paper and reported that it can enhance the physico-chemical capability of the molecules. The F-index and its co-index of the di erent graphs are studied by De et al [5], Milovanovic et al [6] and Basavanagoud et al [7]. Khaksari and Ghorbani [8] studied the certain product of graphs with the same index.…”

Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs

“…There are several study concerning topological indices of different graph operations. In [11], [12] and [13] [17], derived explicit formulae for computing the eccentric-distance sum of different graph operations. Recently, De computes the vertex Zagreb indices of different graph operations in [18].…”