Exponential Fraction Index of Some Interconnection Networks
John Rafael M. Antalan, Noel F. Laoang Jr.

Department of Mathematics and Physics, College of Science, Central Luzon State University (3120), Science City of Munoz, Nueva Ecija, Philippines

Abstract

Topological Indices have many applications in theoretical chemistry. It is used to calculate the sum of the shortest path between molecules, determine the total number of independent sets and matchings, and more that is useful in developing quantitative structure-activity relationships (QSAR). As new molecules and more complex graphs evolve, Prakasha and Kiran introduced the Exponential Fraction index (a degree-based index) defined as EF(G)=&#8721-_(uv&#8712-E(G))e^(du/dv) where du and dv are the maximum and minimum degrees, respectively. Moreover, Praksha and Kiran calculated the Exponential Fraction index of double graphs, subdivision graphs, complements of some standard graphs, and the index for chemical structures of Graphene and Carbon nanocones.

This paper aims to provide additional results to the emerging topological index. We calculated the Exponential Fraction index of the Honeycomb network, Hexagonal network, Rhombus Oxide network, Regular Triangulate Oxide network, Dominating Oxide network, Regular Triangulate Silicate network, and Dominating Silicate network.

Keywords: Exponential Fraction Index, Honeycomb network, Hexagonal network, Rhombus Oxide network, Regular Triangulate Oxide network, Dominating Oxide network, Regular Triangulate Silicate network, Dominating Silicate network

Topic: MATHEMATICS AND STATISTICS