Abstract PQ-type adjacency polytopes $$\nabla ^PQ _G$$ ∇ P Q G are lattice arising from finite graphs G . There is a connection between and the engineering problem known as power-flow study,...

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...

We introduce new labeling called m-bonacci graceful labeling. A graph G on n edges is if the vertices can be labeled with distinct integers from set {0,1,2,…,Zn,m} such that derived edge labels are first numbers. show complete graphs, bipartite gear triangular grid and wheel graphs not graceful. Almost all trees give to cycles, friendship polygonal snake double graphs.

In [J Combin Theory Ser B, 26 (1979), 205–216], Jaeger showed that every graph with 2 edge-disjoint spanning trees admits a nowhere-zero 4-flow. In [J Combin Theory Ser B, 56 (1992), 165–182], Jaeger et al. extended this result by showing that, if A is an abelian group with |A| = 4, then every graph with 2 edgedisjoint spanning trees is A-connected. As graphs with 2 edge-disjoint spanning trees...

tillage and press wheel weight play an important role in seedling emergence, crop establishment and growth. an optimal combination of tillage implements and suitable press wheel weights should increase grain yield. this study investigated the effect of tillage systems and press wheel weights on dry land wheat (triticum aestivum l.) seedling emergence and grain yields in izeh, khuzestan province...

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.

Wheel wear has been a concern in the railway for several decades. Studying the form change of the wheel/rail contacts in particular railways consisting of sharp curves helps to identify the risk of severe or catastrophic wear to minimize maintenance costs in order to be competitive in the transportation business. In this paper, the wheel/rail contact was studied on the particular railways. The ...