we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

By proposing two questions on total colorings of cubic graphs of large girth, we investigate a possible connection between girth and total chromatic parameters in cubic graphs.

A k–bisection of a bridgeless cubic graph G is a 2–colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes (monochromatic components in what follows) have order at most k. Ban and Linial conjectured that every bridgeless cubic graph admits a 2–bisection except for the Petersen graph. A sim...

Yutsis graphs are connected simple graphs which can be partitioned into two vertex-induced trees. Cubic Yutsis graphs were introduced by Jaeger as cubic dual Hamiltonian graphs, and these are our main focus. Cubic Yutsis graphs also appear in the context of the quantum theory of angular momenta, where they are used to generate summation formulae for general recoupling coefficients. Large Yutsis...

Let v(G) and γ(G) denote the number of vertices and the domination number of a graph G, respectively, and let ρ(G) = γ(G)/v(G). In 1996 B. Reed conjectured that ifG is a cubic graph, then γ(G) ≤ ⌈v(G)/3⌉. In 2005 A. Kostochka and B. Stodolsky disproved this conjecture for cubic graphs of connectivity one and maintained that the conjecture may still be true for cubic 2-connected graphs. Their mi...

We are writing this paper as a response to a paper appeared in PFLDnet 2007 authored by Leith et al. on the analysis of CUBIC [1] (hereafter called LSM). There are a few debatable issues that might mislead readers about the behavior of CUBIC. In general, the authors presented their observations on the performance of CUBIC under a special set of testing environments. However, as this paper is ab...

Let v(G) and γ(G) denote the number of vertices and the domination number of a graph G, respectively, and let ρ(G) = γ(G)/v(G). In 1996 B. Reed conjectured that if G is a cubic graph, then γ(G) ≤ dv(G)/3e. In 2005 A. Kostochka and B. Stodolsky disproved this conjecture for cubic graphs of connectivity one and maintained that the conjecture may still be true for cubic 2-connected graphs. Their m...

The objective of this paper is to study the effect of the internal transducer resistance on the dynamic behaviour and the output power of an energy harvester when it is attached to a cubic load resistance. It is seen that by considering the internal resistance, the dynamic equation of a conventional nonlinear energy harvester changes so that it is not easy to separate the linear damping from th...

This thesis provides strong evidence that the quartet distance between two general trees is practically computable in sub-cubic time. The thesis comprises a detailed study of three algorithms for quartet distance computation between trees of arbitrary degree; a quartic, a cubic and a sub-cubic time algorithm. A common property to these three algorithms is that they all have a time complexity th...