AbstractThe Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) over all edges uv of G, where d(u) denotes the degree of a vertex u in G. Caporossi and Hansen proposed a conjecture on the relation between the Randić index R(G) and the chromatic number χ(G) of a graph G: for any connected graph G of order n≥2, R(G)≥χ(G)−22+1n−1(χ(G)−1+n−χ(G)), and furthermore the bound is sharp for all n and 2≤χ(G)≤n. We prove this conjecture
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
© 2016 Elsevier B.V. The variation of the Randić index R′(G) of a graph G is defined by R′(G)=∑uv∈E...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
AbstractThe Randić index R(G) of a graph G=(V,E) is the sum of (d(u)d(v))−1/2 over all edges uv∈E of...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv(d(u)d(v))−12, where d(u) is the de...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
AbstractThe general Randić index of a molecular graph G is the sum of [d(u)d(v)]α over all edges uv∈...
AbstractLet G(k,n) be the set of connected simple n-vertex graphs with minimum vertex degree k. The ...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
The Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) for all edges uv...
The general Randic index R(G) of a graph G is dened as the sum of the weights (d(u)d(v)) of all edg...
The Randić index of a graph G is the sum of ((d(u))(d(v))) α over all edges uv of G, where d(v) deno...
AbstractThe higher Randić index Rt(G) of a simple graph G is defined asRt(G)=∑i1i2⋯it+11δi1δi2⋯δit+1...
AbstractThe Randić index R(G) of a nontrivial connected graph G is defined as the sum of the weights...
Suppose G is a simple graph with edge set EG. The Randić index RG is defined as RG=∑uv∈EG1/degGudegG...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
© 2016 Elsevier B.V. The variation of the Randić index R′(G) of a graph G is defined by R′(G)=∑uv∈E...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
AbstractThe Randić index R(G) of a graph G=(V,E) is the sum of (d(u)d(v))−1/2 over all edges uv∈E of...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv(d(u)d(v))−12, where d(u) is the de...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
AbstractThe general Randić index of a molecular graph G is the sum of [d(u)d(v)]α over all edges uv∈...
AbstractLet G(k,n) be the set of connected simple n-vertex graphs with minimum vertex degree k. The ...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
The Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) for all edges uv...
The general Randic index R(G) of a graph G is dened as the sum of the weights (d(u)d(v)) of all edg...
The Randić index of a graph G is the sum of ((d(u))(d(v))) α over all edges uv of G, where d(v) deno...
AbstractThe higher Randić index Rt(G) of a simple graph G is defined asRt(G)=∑i1i2⋯it+11δi1δi2⋯δit+1...
AbstractThe Randić index R(G) of a nontrivial connected graph G is defined as the sum of the weights...
Suppose G is a simple graph with edge set EG. The Randić index RG is defined as RG=∑uv∈EG1/degGudegG...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
© 2016 Elsevier B.V. The variation of the Randić index R′(G) of a graph G is defined by R′(G)=∑uv∈E...
AbstractThe Randić index R(G) of a graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
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