On a conjecture about the Randić index
نویسندگان
چکیده
منابع مشابه
On the Higher Randić Index
Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih v v v over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...
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The Randić index R(G) of a graph G is defined by R(G) = ∑ uv 1 √ d(u)d(v) , where d(u) is the degree of a vertex u in G and the summation extends over all edges uv of G. Aouchiche et al. proposed a conjecture on the relationship between the Randić index and the diameter: for any connected graph on n ≥ 3 vertices with the Randić index R(G) and the diameter D(G), R(G) − D(G) ≥ √ 2 − n+1 2 and R(G...
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For an edge uv of a graph G, the weight of the edge e = uv is denoted by w(e) = 1/ √ d(u)d(v). Then
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The Randić index of a graph G is defined as R(G) = ∑ u∼v (d(u)d(v))− 2 , where d(u) is the degree of vertex u, and the summation goes over all pairs of adjacent vertices u, v. A conjecture of R(G) for connected graph with n vertices is as follows: R(G)−D √2− n+1 2 and R(G) D 1 2 + √ 2−1 n−1 , where D is the diameter of G. In this paper, we prove that this conjecture is true for unicyclic graphs.
متن کاملon the higher randić index
let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih v v vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.06.025