Weighted-1-antimagic graphs of prime power order

AbstractSuppose G is a graph, k is a non-negative integer. We say G is weighted-k-antimagic if for any vertex weight function w:V→N, there is an injection f:E→{1,2,…,∣E∣+k} such that for any two distinct vertices u and v, ∑e∈E(v)f(e)+w(v)≠∑e∈E(u)f(e)+w(u). There are connected graphs G≠K2 which are not weighted-1-antimagic. It was asked in Wong and Zhu (in press) [13] whether every connected graph other than K2 is weighted-2-antimagic, and whether every connected graph on an odd number of vertices is weighted-1-antimagic. It was proved in Wong and Zhu (in press) [13] that if a connected graph G has a universal vertex, then G is weighted-2-antimagic, and moreover if G has an odd number of vertices, then G is weighted-1-antimagic. In this paper, by restricting to graphs of odd prime power order, we improve this result in two directions: if G has odd prime power order pz and has total domination number 2 with the degree of one vertex in the total dominating set not a multiple of p, then G is weighted-1-antimagic. If G has odd prime power order pz, p≠3 and has maximum degree at least ∣V(G)∣−3, then G is weighted-1-antimagic

Fuzzy EOQ Model with Trapezoidal and Triangular Functions Using Partial Backorder

EOQ fuzzy model is EOQ model that can estimate the cost from existing information. Using trapezoid fuzzy functions can estimate the costs of existing and trapezoid membership functions has some points that have a value of membership . TR ̃C value results of trapezoid fuzzy will be higher than usual TRC value results of EOQ model . This paper aims to determine the optimal amount of inventory in the company, namely optimal Q and optimal V, using the model of partial backorder will be known optimal Q and V for the optimal number of units each time a message . EOQ model effect on inventory very closely by using EOQ fuzzy model with triangular and trapezoid membership functions with partial backorder. Optimal Q and optimal V values for the optimal fuzzy models will have an increase due to the use of trapezoid and triangular membership functions that have a different value depending on the requirements of each membership function value. Therefore, by using a fuzzy model can solve the company's problems in estimating the costs for the next term

Group Irregularity Strength of Connected Graphs

We investigate the group irregularity strength ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group \gr of order $s$, there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels at every vertex are distinct. We prove that for any connected graph $G$ of order at least 3, $s_g(G)=n$ if $n\neq 4k+2$ and $s_g(G)\leq n+1$ otherwise, except the case of some infinite family of stars

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION!!!

The full content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition