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Article
EDGE EXTENSION OF GRAPHS AND DIGRAPHS
توسيـــــــع الحــواف للبيــانات والبيــانات المتجــهــه

Author: Akram B. Attar د.اكرم برزان عطار
Journal: Journal of Education for Pure Science مجلة التربية للعلوم الصرفة ISSN: 20736592 Year: 2011 Volume: 1 Issue: 3 Pages: 54-61
Publisher: Thi-Qar University جامعة ذي قار

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Abstract


Abstract

In this paper, the concepts of edge(arc) extension of graphs(digraphs) and the edge(arc) extensible class of graphs(digraphs) have been introduced. The classes of regular and eulerian graphs(digraphs) which are not edge(arc) extensible classes have also been introduced.
The concept of edge(arc) extensibility number has been introduced as well as the characterization of extensibility number of regular graphs(digraphs). Also the extensibility number of eulerian graphs(digraphs) has been characterized.
Key words: Joining graphs, Extension of graphs, Regular graphs, Reducibility, Contractibility, and Connectivity



الملخـص

في هذا البحث تم تقديم مفهوم توسيع البيانات باضافة حواف جديدة ودراسة البيانات القابلة للتوسيع والغير قابلة للتوسيع. كذلك تم تقديم مفهوم عدد التوسيع للبيانات وإيجاد قيمته للبيانات المنتظمة وبيانات اويلر.



في هذا البحث تم تقديم مفهوم توسيع البيانات باضافة حواف جديدة ودراسة البيانات القابلة للتوسيع والغير قابلة للتوسيع. كذلك تم تقديم مفهوم عدد التوسيع للبيانات وإيجاد قيمته للبيانات المنتظمة وبيانات اويلر.


Article
Resultant Graphs of Block Designs

Authors: G. H. Shirdel --- A. Asgari
Journal: Iraqi Journal of Science المجلة العراقية للعلوم ISSN: 00672904/23121637 Year: 2018 Volume: 59 Issue: 4C Pages: 2317-2322
Publisher: Baghdad University جامعة بغداد

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Abstract

In this paper we have made different regular graphs by using block designs. In one of our applicable methods, first we have changed symmetric block designs into new block designs by using a method called a union method. Then we have made various regular graphs from each of them. For symmetric block designs with λ=1 (which is named finite projective geometry), this method leads to infinite class of regular graphs. With some examples we will show that these graphs can be strongly regular or semi-strongly regular. We have also propounded this conjecture that if two semi-symmetric block designs are non-isomorphic, then the resultant block graphs of them are non-isomorphic, too.

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