Grafovi čija je najmanja karakteristična vrednost minimalna u nekim klasama grafova

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

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

The Laplacian spread of Cactuses

CombinatoricsConnected graphs in which any two of its cycles have at most one common vertex are called cactuses. In this paper, we continue the work on Laplacian spread of graphs, and determine the graph with maximal Laplacian spread in all cactuses with n vertices