Molecular Descriptors and Topological Analysis of Cyclooctane Derivatives

Cyclooctane is mainly used in the synthesis of cyclooctanone, cyclooctanol, caprolactam and octanoic acid. At the same time, it can also be used as an intermediate in organic synthesis and a chemical reagent. By discussing the resistance distance between any two points of cyclooctane derivative Tn(C8), some invariants about resistance distance are obtained, such as Kirchhoff index, multiplicative degree-Kirchhoff index, and additive degree-Kirchhoff index. Topological index can help scholars better understand some physical and chemical properties of compounds, and we obtain the closed expressions of valency-based topological indices for Tn(C8), such as ABC index, GA index, etc.

Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance

Let G = V , E be a connected graph. The resistance distance between two vertices u and v in G , denoted by R G u , v , is the effective resistance between them if each edge of G is assumed to be a unit resistor. The degree resistance distance of G is defined as D R G = ∑ u , v ⊆ V G d G u + d G v R G u , v , where d G u is the degree of a vertex u in G and R G u , v is the resistance distance between u and v in G . A bicyclic graph is a connected graph G = V , E with E = V + 1 . This paper completely characterizes the graphs with the second-maximum and third-maximum degree resistance distance among all bicyclic graphs with n ≥ 6 vertices.

The Hermitian Kirchhoff Index and Robustness of Mixed Graph

Large-scale social graph data poses significant challenges for social analytic tools to monitor and analyze social networks. The information-theoretic distance measure, namely, resistance distance, is a vital parameter for ranking influential nodes or community detection. The superiority of resistance distance and Kirchhoff index is that it can reflect the global properties of the graph fairly, and they are widely used in assessment of graph connectivity and robustness. There are various measures of network criticality which have been investigated for underlying networks, while little is known about the corresponding metrics for mixed networks. In this paper, we propose the positive walk algorithm to construct the Hermitian matrix for the mixed graph and then introduce the Hermitian resistance matrix and the Hermitian Kirchhoff index which are based on the eigenvalues and eigenvectors of the Hermitian Laplacian matrix. Meanwhile, we also propose a modified algorithm, the directed traversal algorithm, to select the edges whose removal will maximize the Hermitian Kirchhoff index in the general mixed graph. Finally, we compare the results with the algebraic connectivity to verify the superiority of the proposed strategy.

Specifying Resistance Distance and Ratio for Special Strength Test in 1500 m Youth Running

The research aimed at specifying distance and ratio of resistance for special strength endurance in 1500m youth running. The researchers used the descriptive method on (30) youth runners from the national center for gifted in Athletics. Three tests were specified and a pilot study was applied to come up with the conclusions and recommended generalizing the distances and ratios specified to test and train special strength endurance for 1500m youth running as well as using these tests for special strength endurance for continuous evaluation of runners and for runner’s selections.