Ramadan El-Shanawany - Academia.edu (original) (raw)

Papers by Ramadan El-Shanawany

British Journal of Applied Science & Technology, 2014

We are concerned with the cartesian products of any finite number of symmetric starter vectors of... more We are concerned with the cartesian products of any finite number of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and use this method to construct ODCs by new infinite classes of disjoint unions of complete bipartite graphs.

Biomedical Signal Processing and Control

ERJ. Engineering Research Journal, Oct 1, 2005

An Orthogonal Double Cover (ODC) of the complete graph is a set of graphs such that every two of ... more An Orthogonal Double Cover (ODC) of the complete graph is a set of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. We consider the case where the graph to be covered twice is the complete bipartite graphs, and all graphs in the collection are isomorphic to the spanning subgraph G (union of certain stars).

British Journal of Mathematics & Computer Science, 2013

In this article, a technique to construct cyclic orthogonal double covers (CODCs) of regular circ... more In this article, a technique to construct cyclic orthogonal double covers (CODCs) of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K 1,2n−10 is introduced. c

An orthogonal double cover (ODC) of a graph is a collection = { ∶ ∈ ()} of | ()| subgraphs (pages... more An orthogonal double cover (ODC) of a graph is a collection = { ∶ ∈ ()} of | ()| subgraphs (pages) of , such that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC of is cyclic (CODC) if the cyclic group of order | ()| is a subgroup of the automorphism group of. In this paper we are concerned with CODC of circulant graphs by a special class of trees and a special class of connected graphs.

We construct orthogonal double covers of Kn,n by Pm+1 ∪ ∗ Sn−m, where n and m are integers, 2 ≤ m... more We construct orthogonal double covers of Kn,n by Pm+1 ∪ ∗ Sn−m, where n and m are integers, 2 ≤ m ≤ 10 ,m ≤ n and Pm+1 ∪ ∗ Sn−m is a tree obtained from the path Pm+1 with m edges and a star Sn−m with n − m edges by identifying an end-vertex of Pm+1 with the center of Sn−m.

Menoufia Journal of Electronic Engineering Research, 2006

An Orthogonal Double Cover of the complete graph is a set of graphs such that every two of them s... more An Orthogonal Double Cover of the complete graph is a set of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper we have constructed the ODC of the complete bipartite graph (), for any values of , and all graphs in the collection are isomorphic to the spanning sub-graph

Prikladnaya Diskretnaya Matematika, 2019

The existing problem of the orthogonal double covers of the graphs is well-known in the theory of... more The existing problem of the orthogonal double covers of the graphs is well-known in the theory of combinatorial designs. In this paper, a new technique called the one edge algorithm for constructing the orthogonal double covers of the complete bipartite graphs by copies of a graph is introduced. The advantage of this algorithm is that it is accessible to discrete mathematicians not intimately familiar with the theory of the orthogonal double covers.

AKCE International Journal of Graphs and Combinatorics, 2015

An orthogonal double cover (ODC) of a graph H is a collection G = {G v : v ∈ V (H)} of |V (H)| su... more An orthogonal double cover (ODC) of a graph H is a collection G = {G v : v ∈ V (H)} of |V (H)| subgraphs of H such that every edge of H is contained in exactly two members of G and for any two members G u and G v in G, |E(G u) ∩ E(G v)| is 1 if u and v are adjacent in H and it is 0 if u and v are nonadjacent in H. In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs for new graph classes. c

British Journal of Mathematics & Computer Science, 2014

Let X be a graph on n vertices and let B = {P (x) : x ∈ V (X)} be a collection of n subgraphs of ... more Let X be a graph on n vertices and let B = {P (x) : x ∈ V (X)} be a collection of n subgraphs of X, one for each vertex, B is an orthogonal double cover (ODC) of X if every edge of X occurs in exactly two members of B and any two members share an edge whenever the corresponding vertices are adjacent in X and share no edges whenever the corresponding vertices are nonadjacent in X. The main question is: given the pair (X, G), is there an ODC of X by G? An obvious necessary condition is that X is a regular. In this paper, we are almost exclusively concerned with the starter maps of the orthogonal double covers of cayley graphs and using this method to construct ODCs by a complete bipartite graph, a complete tripartite graph, caterpillar, and a connected union of a cycle and a star whose center vertex belongs to that cycle.

Ain Shams Engineering Journal, 2015

Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex, G is ... more Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex, G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in H and share no edges whenever the corresponding vertices are nonadjacent in H. In this paper, we are concerned with symmetric starter vectors of the orthogonal double covers (ODCs) of the complete bipartite graph and using the method of cartesian product of symmetric starter vectors to construct ODC of the complete bipartite graph by G, where G is a complete bipartite graph, disjoint union of different complete bipartite graphs and disjoint union of finite copies of a complete bipartite graph.

International Journal of Mathematics and Mathematical Sciences, 2013

LetHbe a graph onnvertices and𝒢a collection ofnsubgraphs ofH, one for each vertex, where𝒢is an or... more LetHbe a graph onnvertices and𝒢a collection ofnsubgraphs ofH, one for each vertex, where𝒢is an orthogonal double cover (ODC) ofHif every edge ofHoccurs in exactly two members of𝒢and any two members share an edge whenever the corresponding vertices are adjacent inHand share no edges whenever the corresponding vertices are nonadjacent inH. In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs by new disjoint unions of complete bipartite graphs.

Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex. Then ... more Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex. Then G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members of G share exactly an edge whenever the corresponding vertices are adjacent in H. If all subgraphs in G are isomorphic to a given spanning subgraph G, then G is said to be an ODC of H by G. We construct ODCs of H = Kn,n by G = Cm ∪v Sn−m (union of a cycle Cm and a star Sn−m whose center vertex v belongs to that cycle and m = 6, 8, 10, 12 and m < n). Furthermore, we construct ODCs of H = Kn,n by G = Cm∪Sn−m (disjoint union of a cycle and a star) where m = 4, 8 and m < n. In all cases, G is a symmetric starter of the cyclic group of order n. In addition, we introduce a generalization of this result.

2021 International Conference on Electronic Engineering (ICEEM)

Menoufia Journal of Electronic Engineering Research

Open Journal of Discrete Mathematics, 2016

of a graph H is a partition of the edge set of H into edgedisjoint subgraphs s

Open Journal of Discrete Mathematics, 2014

An orthogonal double cover (ODC) of a graph H is a collection

Journal of Mathematics Research, 2014

A collection G of isomorphic copies of a given subgraph G of T is said to be orthogonal double co... more A collection G of isomorphic copies of a given subgraph G of T is said to be orthogonal double cover (ODC) of a graph T by G, if every edge of T belongs to exactly two members of G and any two different elements from G share at most one edge. An ODC G of T is cyclic (CODC) if the cyclic group of order |V(T)| is a subgroup of the automorphism group of G. In this paper, the CODCs of infinite regular circulant graphs by certain infinite graph classes are considered, where the circulant graphs are labelled by the Cartesian product of two abelian groups.