title: 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.
authors.affiliation: Department of Basic Sciences and Humanities (Mathematics), Calcutta Institute of Engineering and Management, Kolkata, West Bengal 700 040 India.
authors.forename: Nilanjan
authors.initials: N
authors.lastname: De
authors.affiliation: Department of Mathematics, Aliah University, IIA/27, New Town, Kolkata, West Bengal 700 156 India.
authors.forename: Sk Md Abu
authors.initials: SM
authors.lastname: Nayeem
authors.affiliation: Department of Mathematics, National Institute of Technology, Durgapur, West Bengal India.
authors.forename: Anita
authors.initials: A
authors.lastname: Pal
keywords: F-coindex; F-index; First and second Zagreb indices; Graph operations; Topological index; Vertex degree