Search

The orbit polynomial is a new graph counting polynomial which is defined as OG(x)=&sum, i=1rx|Oi|, where O1, &hellip, Or are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits.

Symmetry is an important visual feature for humans and its application in architecture is completely evident. This paper aims to investigate the role of symmetry in the aesthetics judgment of residential building fa&ccedil, ades and study the pattern of eye movement based on the expertise of subjects in architecture. In order to implement this in the present paper, we have created images in two categories: symmetrical and asymmetrical fa&ccedil, ade images. The experiment design allows us to investigate the preference of subjects and their reaction time to decide about presented images as well as record their eye movements. It was inferred that the aesthetic experience of a building fa&ccedil, ade is influenced by the expertise of the subjects. There is a significant difference between experts and non-experts in all conditions, and symmetrical fa&ccedil, ades are in line with the taste of non-expert subjects. Moreover, the patterns of fixational eye movements indicate that the horizontal or vertical symmetry (mirror symmetry) has a profound influence on the observer&rsquo, s attention, but there is a difference in the points watched and their fixation duration. Thus, although symmetry may attract the same attention during eye movements on fa&ccedil, ade images, it does not necessarily lead to the same preference between the expert and non-expert groups.

Intelligent cooperative multiagent systems are applied for solving a large range of real-life problems, including in domains like biology and healthcare. There are very few metrics able to make an effective smeasure of the machine intelligence quotient. The most important drawbacks of the designed metrics presented in the scientific literature consist in the limitation in universality, accuracy, and robustness. In this paper, we propose a novel universal metric called MetrIntSimil capable of making an accurate and robust symmetric comparison of the similarity in intelligence of any number of cooperative multiagent systems specialized in difficult problem solving. The universality is an important necessary property based on the large variety of designed intelligent systems. MetrIntSimil makes a comparison by taking into consideration the variability in intelligence in the problem solving of the compared cooperativemultiagent systems. It allows a classification of the cooperativemultiagent systems based on their similarity in intelligence. A cooperative multiagent system has variability in the problem solving intelligence, and it can manifest lower or higher intelligence in different problem solving tasks. More cooperative multiagent systems with similar intelligence can be included in the same class. For the evaluation of the proposed metric, we conducted a case study for more intelligent cooperative multiagent systems composed of simple computing agents applied for solving the Symmetric Travelling Salesman Problem (STSP) that is a class of NP-hard problems. STSP is the problem of finding the shortest Hamiltonian cycle/tour in a weighted undirected graph that does not have loops or multiple edges. The distance between two cities is the same in each opposite direction. Two classes of similar intelligence denoted IntClassA and IntClassB were identified. The experimental results show that the agent belonging to IntClassA intelligence class is less intelligent than the agents that belong to the IntClassB intelligence class. publishedVersion

Shannon entropies for networks have been widely introduced. However, entropies for weighted graphs have been little investigated. Inspired by the work due to Eagle et al., we introduce the concept of graph entropy for special weighted graphs. Furthermore, we prove extremal properties by using elementary methods of classes of weighted graphs, and in particular, the one due to Bollobás and Erdös, which is also called the Randi´c weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.