Add to ORKGFor a connected undirected graph $G=(V,E)$ with vertex set $\{1, 2, \ldots, n\}$ and degrees $ d_i$, for $1\le i \le n$, we show that $$ABC(G) \le \sqrt{(n-1)(|E|-R_{-1}(G))},$$ where $\displaystyle R_{-1}(G)=\sum_{(i,j)\in E}\frac{1}{d_id_j}$ is the Randi\'c index. This bound allows us to obtain some maximal results for the $ABC$ index with elementary proofs and to improve all the upper bounds in [20], as well as some in [17], using lower bounds for $R_{-1}(G)$ found in the literature and some new ones found through the application of majorization
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 graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
Abstract. Given a simple connected graph on N vertices with size | |E and degree sequence 1 2... Nd ...
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 general Randić index of a molecular graph G is the sum of [d(u)d(v)]α over 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...
AbstractLet G(k,n) be the set of connected simple n-vertex graphs with minimum vertex degree k. The ...
Suppose G is a simple graph with edge set EG. The Randić index RG is defined as RG=∑uv∈EG1/degGudegG...
Abstract The general sum-connectivity index χ α ( G ) $\chi_{\alpha}(G)$ , for a (molecular) graph G...
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 is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
Let G = (V,E) be a simple connected graph with the vertex set V = {1,2,...,n} and sequence of vertex...
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...
Given a simple connected graph on N vertices with size |E| and degree sequence d₁≤d₂≤...≤dn, the a...
AbstractThe Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) over all...
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 graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
Abstract. Given a simple connected graph on N vertices with size | |E and degree sequence 1 2... Nd ...
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 general Randić index of a molecular graph G is the sum of [d(u)d(v)]α over 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...
AbstractLet G(k,n) be the set of connected simple n-vertex graphs with minimum vertex degree k. The ...
Suppose G is a simple graph with edge set EG. The Randić index RG is defined as RG=∑uv∈EG1/degGudegG...
Abstract The general sum-connectivity index χ α ( G ) $\chi_{\alpha}(G)$ , for a (molecular) graph G...
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 is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
Let G = (V,E) be a simple connected graph with the vertex set V = {1,2,...,n} and sequence of vertex...
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...
Given a simple connected graph on N vertices with size |E| and degree sequence d₁≤d₂≤...≤dn, the a...
AbstractThe Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) over all...
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 graph G is defined by R(G)=∑uv1d(u)d(v), where d(u) is the degree...
Abstract. Given a simple connected graph on N vertices with size | |E and degree sequence 1 2... Nd ...