E. M. Badr

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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)
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)
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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