Grafovi čija je najmanja karakteristična vrednost minimalna u nekim klasama grafova

Abstract

Spectral graph theory is an important interdisciplinary field of science and mathematics in which methods of linear algebra are used to solve problems in graph theory. It has numerous applications for modelling problems in chemistry, computers science, medicine, economy, and physics, to name just a few. By representing a graph as an adjacency matrix, matrix theory can be applied to graph theory. Features of the graph can be investigated using the eigenvalues and the eigenvectors of the adjacency matrix, and these give us information about the graph’s structure. The eigenvalues of a graph G can be ordered decreasingly, where the first is denoted by (G) and is called the index of the graph and the least eigenvalue is denoted by (G). A graph’s spread s(G) is defined as the difference between the greatest and the least eigenvalue of the graph’s adjacency matrix, i.e. s(G) = (G) − (G). The principal topic of this doctoral thesis is the least eigenvalue of a graph. The structure of a graph G that has the minimum least eigenvalue within a certain class of graphs is determined. This graph is referred to as an extremal graph.