Vertex of V

A set D of vertices in a graph G(V, E) is a dominating set of G, if every vertex of V not in D is adjacent to at least one vertex in D. A dominating set D of G(V, E)is a k – fair dominating set of G, for

6p lucastanguyen 01-06-2020 5 1   Download

We give a new construction of the moonshine module vertex operator algebra V , which was originally constructed in [FLM2]. We construct it as a framed VOA over the real number field R. We also offer ways to transform a structure of framed VOA into another framed VOA. As applications, we study the five framed VOA structures on VE8 and construct many framed VOAs including V from a small VOA. One of the advantages of our construction is that we are able to construct V as a framed VOA with a positive definite invariant bilinear form and we...

63p tuanloccuoi 04-01-2013 48 7   Download

We propose two alternative measures of the local irregularity of a graph in terms of its vertex degrees and relate these measures to the order and the global irregularity of the graph measured by the difference of its maximum and minimum vertex degree.All graphs will be simple and finite. Let G = (V,E) be a graph of order n = |V |. The degree and the neighbourhood of a vertex u 2 V will be denoted by d(u) and N(u). The maximum and minimum degree of G will be denoted by
(G) and (G).

6p thulanh5 12-09-2011 56 3   Download

Let G be a graph with vertex set V (G) = {1, . . . , n} and edge set E(G). We are interested in studying the functions of the graph G whose values belong to the interval [(G), (G)]. Here (G) is the size of the largest stable set in G and (G) is the smallest number of cliques that cover the vertices of G. It is well known (see, for example, [1]) that for some  0 it is impossible to approximate in polynomial time (G) and (G) within a factor of n, assuming P 6= NP. We suppose that better approximation could...

5p thulanh5 12-09-2011 65 4   Download

A defensive alliance in a graph G = (V,E) is a set of vertices S  V satisfying the condition that for every vertex v 2 S, the number of neighbors v has in S plus one (counting v) is at least as large as the number of neighbors it has in V − S. Because of such an alliance, the vertices in S, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves from the vertices in V − S. A defensive alliance S is called global if it effects every vertex in V − S, that is,...

13p thulanh5 12-09-2011 38 2   Download