The degree distance index (DDI) is a vertex-degree weighted version of well-known that called by Wiener (WI). In extremal theory graphs, improving the bounds with best possible values worth investigating problem. this note, exact formulae DDI for four different types sum graphs in terms various indic...

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Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.

In the silkworm, Bombyx mori, normal markings are mainly controlled by the +P gene, which is located on the second chromosome. Due to a lack of crossing over in females, reciprocal backcrossed F1 (BC1) progenies were used for linkage analysis and mapping of the +P gene based on an SSR linkage map using silkworm strains P50 and H9, which are normal marking and sex-limited marking, respectively. ...

Although the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are affected by the local and global structural properties. Analyzing the data of four large-scale online social networks reveals several common structural properti...

Let S be a polynomial of degree 2n + 2, that is, positive on the real axis, and let w = 1/S on (−∞,∞). We present an explicit formula for the nth orthogonal polynomial and related quantities for the weight w. This is an analogue for the real line of the classical Bernstein-Szegő formula for (−1, 1). 1. The result The Bernstein-Szegő formula provides an explicit formula for orthogonal polynomial...