The competition numbers of ternary Hamming graphs

It is known to be a hard problem to compute the competition number k(G) of a graph G in general. Park and Sano [13] gave the exact values of the competition numbers of Hamming graphs H(n,q) if $1 \leq n \leq 3$ or $1 \leq q \leq 2$. In this paper, we give an explicit formula of the competition numbers of ternary Hamming graphs.Comment: 6 pages, 2 figure

The competition numbers of Hamming graphs with diameter at most three

The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs. In this paper, we compute the competition numbers of Hamming graphs with diameter at most three.Comment: 12 pages, 1 figur

Creative Challenge research report

The exploratory research tries to understand a tripartite relationship between the academic, the creative industry employer and the student and their expectations within it. The role of the student being an important one here in this mix as a embodying academic education and rigour, but also a potential future employee with appropriate enterprise skills. It further tries to understand how an entrepreneurship programme, such as the Creative Challenge, can add value in this relationship and explore its role. From feedback of those students who have participated in the Creative Challenge, we know that it had a whole range of perceived benefits, including the development of new skills, better learning strategies, increased confidence, a clearer understanding of how their creative skills can potentially be applied in the world outside university. Finally the research touches on the relationship between entrepreneurship education and creative arts education

The University of North Carolina at Greensboro Regional Undergraduate Mathematics Conference Abstracts

It was a very chaotic day, says Kathryn Sikes. Indeed, mutants spread everywhere, according to Brian Stadler. Bacterial wars raged all over the place, adds Dan MacMartin. Everybody was stealing, reported Christian Sykes. There were no limits to it, witnessed by Samuel Grundman. Only the fittest survived and got out of the prison, noted by Joseph Krenicky. The group was set free by Steven Piantadosi. We almost got lost in cyclic paths, said Heather Allmond. At least, our weight was a perfect number, smiles Michael Shiver, because we were not oversized thanks to Martha Shott. Finally, a picture was taken by Gavin Taylor and you could win a date if you listened to David Dombrowski. Math can be a lot of fun