In this paper, we used the permutation group together with concept of cordiality in graph theory to introduce a new method labeling. This construed permuted cordial labeling can be applied all paths, cycles, fans and wheel graphs. Moreover, some other properties are investigated show that union any two paths cycles addition, for path cycle.

the single wheel tester is an experimental device used to measure wheel forces when studying the relation of soil and wheel in a soil bin or in the field. in the model under development, a special frame holding the test wheel is connected to a loading carriage by two pairs of vertical rails and four rollers to provide a floating connection. by applying a driving torque to the test wheel shaft, ...

Apart from regular wheel wear such as decreasing wheel diameters and reduced flange thicknesses and heights, wheel flats (WF) and oval wheels (or OOR, Out-Of-Roundness) are the most common wheelset problems for railway vehicles. Within the FP7 Research Project “Saferail”, APT has developed an innovative wheelset monitoring system so-called “Wheel flat and Out of Roundness Monitoring (WORM) syst...

A semi-topological r-wheel, denoted by Sr, is a subdivision of the r-wheel preserving the spokes; the paper describes the r-connected graphs having no Sr-subgraphs. For r > 3, these are shown to be only Kr,r, while the class H of 3-connected S3-free graphs is unexpectedly rich. First, every graph G in H has an efficiently recognizable set of “contractible edges” (sometimes empty) such that a co...

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called local edge antimagic labeling if for any two adjacent edges e uv e’ vw G, we have w(e) ≠ w(e’), where the weight w(e uv) f(u)+f(v) w(e’) f(v)+f(w). has labeling. The chromatic number χ’lea(G) defined to minimum colors taken over all colorings induced by labelings G. In thi...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

We introduce a family of new integrable quantum field theories in four dimensions by considering the γ-deformed N = 4 SYM in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the ’t Hooft limit, these 4D theories are integrable, and conta...

Let n ? 4 . The helm graph H on 2 ? 1 vertices is obtained from the wheel W by adjoining a pendant edge to each vertex of outer cycle Suppose even. D : = [ d i j ] be distance matrix In this paper, we first show that det ( ) 3 Next, find L and vector u such + ? We also prove an interlacing property between eigenvalues