The maximum number of maximal independent sets in unicyclic connected graphs
نویسندگان
چکیده
منابع مشابه
on the number of maximum independent sets of graphs
let $g$ be a simple graph. an independent set is a set ofpairwise non-adjacent vertices. the number of vertices in a maximum independent set of $g$ isdenoted by $alpha(g)$. in this paper, we characterize graphs $g$ with $n$ vertices and with maximumnumber of maximum independent sets provided that $alpha(g)leq 2$ or $alpha(g)geq n-3$.
متن کاملThe number of independent sets in unicyclic graphs
In this paper, we determine upper and lower bounds for the number of independent sets in a unicyclic graph in terms of its order. This gives an upper bound for the number of independent sets in a connected graph which contains at least one cycle. We also determine the upper bound for the number of independent sets in a unicyclic graph in terms of order and girth. In each case we characterize th...
متن کاملThe 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
متن کاملMaximising the number of independent sets in connected graphs
A Turán connected graph TCn,α is obtained from α cliques of size b αc or d αe by joining all cliques by an edge to one central vertex in one of the larger cliques. The graph TCn,α was shown recently by Bruyère and Mélot to maximise the number of independent sets among connected graphs of order n and independence number α. We prove a generalisation of this result by showing that TCn,α in fact ma...
متن کاملIntegers for the Number of Maximal Independent Sets in Graphs
Let G be a simple undirected graph. Denote by mi(G) (respectively, xi(G)) the number of maximal (respectively, maximum) independent sets in G. In this paper we determine the third and fouth largest value of mi(G) among all graphs of order n. Moreover, the extremal graphs achieving these values are also determined. Mathematics Subject Classification: 05C35, 05C69, 68R10
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.07.079