COMPUTATIONAL ANALYSIS OF ENERGY OF SOME OF THE GRAPHS USING MATGRAPH

Abstract

The story begins with an awkward problem whose solution could not be categorized into any known branch of mathematics of the day. Slowly, in the 19th century, more mathematical curiosities began to be lumped into the same category of graphs. By the 20th century, graph theory had become a rigorous field with countless applications in not only mathematics itself but also many scientific disciplines. Graph theory is a mathematical study of graphs. Leonard Euler was the first person to solve a problem scientifically through graphs in 1736. It is the study of graphs through nodes and edges. The birth of graph theory is often considered to have taken place in 1736 when the Swiss mathematician solved a problem of the seven bridges of Konigsberg. Today, graph theory has become one of the most interesting and innovative fields of mathematics. Graph theory is a growing field and is being applied to areas of physics, computer science, pattern studies, and communication networks. Graph theory has a great contribution to the field of chemistry. The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. It is the study of the spectral properties of a graph by studying the characteristic polynomial and eigenvectors of matrices associated with the graph, such as its adjacency matrix. In this study, we will find the energy of the octagonal quadrilateral network with n-quadrilaterals and n-octagons.