Comparison theorems on resistance distances and Kirchhoff indices of the so-called S& T -isomer graphs are established. Then these results are applied to compare Kirchhoff indices of hexagonal chains, showing that the straight chain is the unique chain with maximum Kirchhoff index, whereas the minimum Kirchhoff index is achieved only when the hexagonal chain is an ‘‘all-kink’’ chain. © 2014 Els...

A Polyomino is an edge–connected union of cells in the planar square lattice. Here we consider generalized linear polyominoes; that is, the polyominoes supported by a n × 2 lattice. In this paper, we obtain the Green function and the Kirchhoff index of a generalized linear polyomino as a perturbation of a 2n–path by adding weighted edges between opposite vertices. This approach deeply links gen...

objectives: wheelchairs are the prime mobility aid of persons with spinal cord injuries. manual wheelchair propulsion puts a lot of demand on the cardiopulmonary as well as the skeletal system. the main purpose of the study was to compare the effects of both arm ergometry training and progressive resistance exercise training of upper limbs on resting heart rate and distance covered during wheel...

Let G 1 + G 2 , G 1 • G 2 and G 1 {G 2 } be the join, corona and cluster of graphs G 1 and G 2 , respectively. In this paper, Kirchhoff index formulae of these composite graphs are given.

Let [Formula: see text] be a simple graph. The resistance distance between [Formula: see text], denoted by [Formula: see text], is defined as the net effective resistance between nodes i and j in the corresponding electrical network constructed from G by replacing each edge of G with a resistor of 1 Ohm. The resistance-distance matrix of G, denoted by [Formula: see text], is a [Formula: see tex...

This paper presents the effects of instrument transformers connection points on the measured impedance by distance relays in the presence of Flexible Alternating Current Transmission System (FACTS) devices with series connected branch. Distance relay tripping characteristic itself depends on the power system structural conditions, pre-fault operational conditions, and especially the ground ...

We extend the resistance distance kernel to the domain of signed dissimilarity values, and show how it can be applied to collaborative rating prediction. The resistance distance is a graph kernel inspired by electrical network models where edges of a graph are interpreted as electrical resistances. We model the similarity between users of a large collaborative rating database using this signed ...