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This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will… (More)

- E. M. Badr
- 2012

Graceful and odd gracefulness of a graph are two entirely different concepts. A graph may posses one or both of these or neither. We present four new families of odd graceful graphs. In particular we show an odd graceful labeling of the linear 4 1 kC snake mK − e and therefore we introduce the odd graceful labeling of 4 1 kC snake mK − e (for the general… (More)

- E. M. Badr, M. I. Moussa
- 2013

The aim of this paper is to present some odd graceful graphs. In particular we show that the revised friendship graphs F(kC4), F(kC8), F(kC12), F(kC16) and F(kC20) are odd graceful where k is any positive integer. Finally, we introduce a new conjecture " The revised friendship graph F(kCn) is odd graceful where k is any positive integer and n = 0 (mod 4).

- M. I. Moussa, E. M. Badr
- 2012

An induced subgraph S of a graph G is called a derived subgraph of G if S contains no isolated vertices. An edge e of G is said to be residual if e occurs in more than half of the derived subgraphs of G. We prove some theorems which calculate the number of derived subgraphs for some special graphs. We also present a new algorithm SDSA that calculates the… (More)

- Eid Badr, Rothermel Kurt, M Betreuer, Bilal Sc, Hameed
- 2011

New technologies have a great influence on the production process in modern factories. Introducing new techniques and methods is crucial to optimize and enhance the working of factories. However , ensuring a reliable and correct integration requires complete evaluation and assessment. In this thesis I utilize RFID systems and image processing to develop and… (More)

The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph L n with m-pendant L n mk 1 is odd graceful. We also show that the subdivision of ladder graph… (More)

The objective of this paper is to present a new class of odd graceful graphs. In particular, we show that the linear cyclic snakes (1, k) C4-snake and (2, k) C4-snake are odd graceful. We prove that the linear cyclic snakes (1, k) C6-snake and (2, k) C6-snake are odd graceful. We also prove that the linear cyclic snakes (1, k) C8-snake and (2, k) C8-snake… (More)

- M. I. Moussa, E. M. Badr
- 2013

Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to reduce the number of processors by fraction 1/ () f n and the… (More)

- E. M. Badr
- 2012

The aim of this paper is to present an experimental evaluation of a parallel derived subgraph algorithm PDSA using MPI. The performance of the algorithm PDSA is verified by computational experiments on some special graphs with different size, run in a cluster of workstations. MPI seems to be appropriate for these kind of experiments as the results are… (More)

- M. I. Moussa, E. M. Badr
- 2011

A graph G of size q is odd-graceful, if there is an injection f from V(G) to {0, 1, 2, …, 2q-1} such that, when each edge xy is assigned the label or weight | f(x)-f(y)|, the resulting edge labels are {1, 3, 5, …, 2q-1}. This definition was introduced in 1991 by Gnanajothi [1] who proved that the graphs obtained by joining a single pendant edge to each… (More)

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