Let G be a connected graph with vertex set V (G) and edge set E(G). The eccentric connectivity index of G, denoted by ξc(G), is defined as ∑ v∈V (G) deg(v)ec(v), where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. In this paper, we propose the edge version of the above index, the edge eccentric connectivity index of G, denoted by ξc e(G), which is defined as ξc e(G) = ∑ f∈E(...

Let Sz(G), Sz(G) and W (G) be the Szeged index, revised Szeged index and Wiener index of a graph G. In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order n > 10 are characterized; and the graphs with the first, second, third, and fourth largest Wiener indices among all bicyclic graphs are identified. Based on these results...

In this paper, we compute ABC index, Randic connectivity index, Sum connectivity index, GA index, Harmonic index, General Randic index of Triglyceride. AMS subject classification:

The default-mode network has been reported to possess highly versatile and even contrasting functions but the underlying functioning mechanism remains elusive. In this study, we adopt a dynamic view of the default-mode network structure and hypothesize that it could potentially contribute to different functions through dynamic reorganization of its functional interaction pattern within and acro...

The Wiener index W( G) of a connected graph G is the sum of the distances d( u, v) between all pairs of vertices u and v of G. This index seems to have been introduced in [22] where it was shown that certain physical properties of various paraffin species are correlated with the Wiener index of the tree determined by the carbon atoms of the corresponding molecules. Canfield, Robinson, and Rouvr...

If G is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of G. The edge-Wiener index We of G is then equal to the sum of distances between all pairs of edges of G. We give bounds on We in terms of order and size. In particular we prove the asymptotically sharp upper bound We(G) ≤ 25 55 n5 + O(n9/2) for gr...

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