Enabling universal Internet access is one of the key issues that is currently being addressed globally. However the existing Internet architecture is seriously “challenged” to ensure universal service provisioning. This short paper puts forth our vision to make the Internet more accessible by architecting a universal communication architectural framework combining two emerging architecture and ...

Pervasive environments are comprised of resource-constrained mobile devices “limited” in their connectivity to other devices or networks due to the inherent dynamic nature of the environment. Limited connectivity to the Internet precludes the use of conventional security mechanisms like Certifying Authorities and other forms of server-centric authentication. Under these circumstances peer-to-pe...

The foundation of most intellectual discourse is Western-centric to the exclusion of other views. This includes ideal patterns of social interaction, preference for aesthetic, accepted norms and values, and the concepts of dignity, respectability, morality and ethics. Such a position is culturally myopic. Western cultural influence colors all of them including moral precepts. The assumption is ...

In this paper, we present some new lower and upper bounds for the modified Randic index in terms of maximum, minimum degree, girth, algebraic connectivity, diameter and average distance. Also we obtained relations between this index with Harmonic and Atom-bond connectivity indices. Finally, as an application we computed this index for some classes of nano-structures and linear chains.

The Randić index R(G) of a graph G is the sum of weights (deg(u) deg(v))−0.5 over all edges uv of G, where deg(v) denotes the degree of a vertex v. Let r(G) be the radius of G. We prove that for any connected graph G of maximum degree four which is not a path with even number of vertices, R(G) ≥ r(G). As a consequence, we resolve the conjecture R(G) ≥ r(G)− 1 given by Fajtlowicz in 1988 for the...

The Randić index of a graph G, written R(G), is the sum of 1 √ d(u)d(v) over all edges uv in E(G). Let d and D be positive integers d < D. In this paper, we prove that if G is a graph with minimum degree d and maximum degree D, then R(G) ≥ √ dD d+Dn; equality holds only when G is an n-vertex (d,D)-biregular. Furthermore, we show that if G is an n-vertex connected graph with minimum degree d and...

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...

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

Given a connected graph G, the Randić index R(G) is the sum of 1 √ d(u)d(v) over all edges {u, v} of G, where d(u) and d(v) are the degree of vertices u and v respectively. Let q(G) be the largest eigenvalue of the singless Laplacian matrix of G and n = |V (G)|. Hansen and Lucas (2010) made the following conjecture:

In this paper, we defined a novel delta value di in molecular connectivity, and then obtained a novel kind of valence molecular connectivity index. The potential usefulness of the novel kind of valence molecular connectivity index in QSAR/QSPR is evaluated by its correlation with a number of molecules and by a favorable comparison with models based on molecular connectivity index. q 2003 Elsevi...