On electric resistances for distance-regular graphs

D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs

The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...

Graph Effective Resistance and Distributed Control: Electrical Analogy and Scalability

We introduce the concept of matrix-valued effective resistance for undirected matrix-weighted graphs. These effective resistances are defined to be the square blocks that appear in the diagonal of the inverse of the matrix-weighted Dirichlet graph Laplacian matrix. However, they can also be obtained from a “generalized” electrical network that is constructed from the graph, and for which curren...

Performance of a Single Chamber Soil Microbial Fuel Cell at Varied External Resistances for Electric Power Generation

Distance-Balanced Closure of Some Graphs

In this paper we prove that any distance-balanced graph $G$ with $Delta(G)geq |V(G)|-3$ is regular. Also we define notion of distance-balanced closure of a graph and we find distance-balanced closures of trees $T$ with $Delta(T)geq |V(T)|-3$.

Calculating two-point resistances in distance-regular resistor networks

An algorithm for the calculation of the resistance between two arbitrary nodes in an arbitrary distance-regular resistor network is provided, where the calculation is based on stratification introduced in [1] and Stieltjes transform of the spectral distribution (Stieltjes function) associated with the network. It is shown that the resistances between a node α and all nodes β belonging to the sa...