The number of independent sets of unicyclic graphs with given matching number
نویسندگان
چکیده
منابع مشابه
The Harmonic Index of Unicyclic Graphs with given Matching Number
The harmonic index of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we determine the graph with minimum harmonic index among all unicyclic graphs with a perfect matching. Moreover, the graph with minimum harmonic index among all unicyclic graphs with a given matching num...
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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...
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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 $alpha(g)geq n-3$.
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The 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 ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2012
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.09.007