TRANSACTIONS ON COMBINATORICS
Year:2012 | Volume:1 | Issue:2|Papers Count:6

Abstract S. Kim et al. have been analyzed the girth of some algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes, i.e. Tanner (3; 5) of length 5p, where p is a prime of the form 15m+1. In this paper, by extension this method to Tanner (3; 7) codes of length 7p, where p is a prime of the form 21m+1, the girth values of Tanner (3; 7) codes will be derived. As an advantage, the rate of Tanner (3; 7) codes is about 0: 17 more than the rate of Tanner (3; 5) codes.

A dominating set DÍV of a graph G= (V; E) is said to be a connected cototal dominating set if (D) is connected and (V-D) ¹f, contains no isolated vertices. A connected cototal dominating set is said to be minimal if no proper subset of D is connected cototal dominating set. The connected cototal domination number (G) of G is the minimum cardinality of a minimal connected cototal dominating set of G. In this paper, we begin an investigation of connected cototal domination number and obtain some interesting results.

Let G be a connected graph with vertex set V (G). The degree resistance distance of G is defined as DR (G) = S(u,v)ÍV (G) [d (u)+d (v)] R (u; v), where d (u) is the degree of vertex u, and R (u; v) denotes the resistance distance betweenu and v. In this paper, we characterize n-vertex unicyclic graphs having minimum and second minimum degree resistance distance.

The non commuting graphr Ñ(G) of a non-abelian fnite group G is defined as follows: its vertex set is G - Z (G) and two distinct vertices x and y are joined by an edge if and only if the commutator of x and y is not the identity. In this paper we prove some new results about this graph. In particular we will give a new proof of Theorem 3.24 of [A. Abdollahi, S. Akbari, H. R, Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) 468-492.]. We also prove that if G1; G2;…; Gn are finite groups such that Z (Gi) =1 for i=1; 2;… ; n and they are characterizable by non commuting graph, then G1xG2x…xGn is characterizable by non-commuting graph.

Let G be a simple graph of order n. We consider the independence polynomial and the domination polynomial of a graph G. The value of a graph polynomial at a specific point can give sometimes a very surprising information about the structure of the graph. In this paper we investigate independence and domination polynomial at -1 and 1.

In this paper we introduce the concept of order di erence interval graph GODI (G) of a groupG. It is a graph GODI (G) with V (GODI (G)) =G and two vertices a and b are adjacent in GODI (G) if and only if o (b)- o (a) Î [o (a); o (b)]. Without loss of generality, we assume that o (a) £ o (b). In this paper we obtain several properties of GODI (G), upper bounds on the number of edges of GODI (G) and determine those groups whose order di erence interval graph is isomorphic to a complete multipartite graph.