on the number of maximum independent sets of graphs

On the number of maximum independent sets in Doob graphs

The Doob graph D(m,n) is a distance-regular graph with the same parameters as the Hamming graph H(2m+n, 4). The maximum independent sets in the Doob graphs are analogs of the distance-2 MDS codes in the Hamming graphs. We prove that the logarithm of the number of the maximum independent sets in D(m,n) grows as 2(1+o(1)). The main tool for the upper estimation is constructing an injective map fr...

Towards Maximum Independent Sets on Massive Graphs

Maximum independent set (MIS) is a fundamental problem in graph theory and it has important applications in many areas such as social network analysis, graphical information systems and coding theory. The problem is NP-hard, and there has been numerous studies on its approximate solutions. While successful to a certain degree, the existing methods require memory space at least linear in the siz...

INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS

Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$,  if no two vertices of $S$ are adjacent.The  independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.

On maximum number of minimal dominating sets in graphs

the effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)

cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...

The Maximum Number of Maximal Independent Sets in Forests

Let G be a simple and undirected graph. By mi(G) we denote the number of maximal independent sets in G. In this note, we determine the maximum number of maximal independent sets among the set of a type of forests. Mathematics Subject Classification: 05C05; 05C50; 05C69