Representation of competitions by complex neutrosophic information

The concept of generalized complex neutrosophic graph of type 1 is an extended approach of generalized neutrosophic graph of type 1. It is an effective model to handle inconsistent information of periodic nature. In this research article, we discuss certain notions, including isomorphism, competition graph, minimal graph and competition number corresponding to generalized complex neutrosophic graphs. Further, we describe these concepts by several examples and present some of their properties. Moreover, we analyze that a competition graph corresponding to a generalized complex neutrosophic graph can be represented by an adjacency matrix with suitable real life examples. Also, we enumerate the utility of generalized complex neutrosophic competition graphs for computing the strength of competition between the objects. Finally, we highlight the significance of our proposed model by comparative analysis with the already existing models.

Competition Numbers and Phylogeny Numbers of Connected Graphs and Hypergraphs

Let D be a digraph. The competition graph of D is the graph having the same vertex set with D and having an edge joining two different vertices if and only if they have at least one common out-neighbor in D. The phylogeny graph of D is the competition graph of the digraph constructed from D by adding loops at all vertices. The competition/phylogeny number of a graph is the least number of vertices to be added to make the graph a competition/phylogeny graph of an acyclic digraph. In this paper, we show that for any integer k there is a connected graph such that its phylogeny number minus its competition number is greater than k. We get similar results for hypergraphs.

q-Rung Orthopair Fuzzy Competition Graphs with Application in the Soil Ecosystem

The q-rung orthopair fuzzy set is a powerful tool for depicting fuzziness and uncertainty, as compared to the Pythagorean fuzzy model. The aim of this paper is to present q-rung orthopair fuzzy competition graphs (q-ROFCGs) and their generalizations, including q-rung orthopair fuzzy k-competition graphs, p-competition q-rung orthopair fuzzy graphs and m-step q-rung orthopair fuzzy competition graphs with several important properties. The study proposes the novel concepts of q-rung orthopair fuzzy cliques and triangulated q-rung orthopair fuzzy graphs with real-life characterizations. In particular, the present work evolves the notion of competition number and m-step competition number of q-rung picture fuzzy graphs with algorithms and explores their bounds in connection with the size of the smallest q-rung orthopair fuzzy edge clique cover. In addition, an application is illustrated in the soil ecosystem with an algorithm to highlight the contributions of this research article in practical applications.

From a Static to a Dynamic Perspective in Handball Match Analysis: a Systematic Review

The aim of this study was to perform a systematic review of the scientific literature on handball match analysis and to identify potential research areas for future work. Data were collected from Web of Science, MEDLINE, SPORTDiscus, Scopus, EBSCO, and ProQuest databases. The initial search found 148 journal articles. Only the papers focused on handball match analysis regarding tactical and technical aspects were considered, for a final list of 25 publications. The complexity approach under which each considered publication was conducted was taken into account (i.e., static vs. dynamic). Therein, authors, main analysis, number of performance indicators under study, considered situational variables, statistics and/or analysis methods, type of competition, number of matches, and sex of participants were distinguished for classification purposes. Research on handball match analysis has evolved over the years, mainly due to the great technological advances. Studies conducted under the classical static complexity approach are the most extended. Studies performed under the relatively new dynamic complexity approach are growing. The present review identified the following main guidelines for future work on handball match analysis: conducting more studies focused on the defensive profile; analyzing handball national leagues and international club competitions; performing more studies in female handball; including game situational variables into the analysis (i.e., game type, match status, game location, quality of opposition, game period); incorporating critical events of the game into the analysis (e.g., team timeouts, exclusions); and, conducting further research from the promising dynamic complexity perspective.

The competition number of a generalized line graph is at most two

Graph Theory International audience In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this paper, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient conditions for the competition number of a generalized line graph being one.