An edge dominating set of a graph is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G. The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domination value is defined. Further, the exact values of the above said parameters are found for some standard classes of graphs. The bounds of the co-odd (even) sum degree edge domination number are obtained in terms of basic graph terminologies. The co-odd (even) sum degree edge dominating sets are characterized. The relationships with other edge domination parameters are also studied.
الملخص الضاد والظاء موطن تفرّد العربية وفخرها ، ألّفت فيهما العشرات والعشرات من المصنّفات الثرّة لكثرة ذرائع تلابسهما والخلط بينهما ، فهما متشابهان في هيكل البناء ، وإخراجهما متداخل على اللسان ، وألفاظهما متناظرة برحابة في الإملاء ، فضلاً عن سريان إشكالهما إلى حدّ الآن ، مما حثّني على التفكير في وسائل تسهّل المطروح وتمدّ جسراً بين أجزائه عسى أن تدنو قِطافُهُ في دفع الشبهة ومواراتها ، فتحصّلت لي أمور أذعتُها
... Show MoreThe research aims to explain the stage of recording Qur’anic readings in the blogs and writings of other sciences until it reached an independent, integrated science based on its principles, for which separate books were devoted to it, because of the necessity of highlighting that stage in which the science of Qur’anic readings overlapped with the blogs of other sciences. Because it relates to the gradual maturity of this science and its historical paths, the goal of the research is achieved by answering questions, the most important of which are: What are the science records in which Quranic readings were found, and what are the books that were unique to writing about this science. The researcher followed the inductive and desc
... Show MoreThe costume is a language that has carved itself into a path that is transformed over time in line with the development of human thought. The child theater is a form of communication between the individual and his society. The costume in the child's theater is seen as a sign of personality and identity. It is a model of communication that uses many of the world systems to which it belongs. Directed to the child by invoking the creative and creative energies of the designer in the formation of the children's theater. The second topic was the communicative function of secondary signs of uniforms and patterns of their transformations. The theoretical framework of the indicators included the on the research community. And his tools in the an
... Show MoreThe comparative literature is a branch of literary criticism which Point to the literary association and relation connecting a mong different world nations and the effect of a nations literature and Culture on another nations literature and culture .So the comparative literature is an image and affront of influence on another nation and countrys literature and culure, for example, the effect of Arabic literature on the Persian , French , English Turkish, Indian and Chinese literature and vice aversa . The current research includes three sections .The first section refers to the meaning and definition of the term “comparative literature '', its origin and beginning s. While the second section focuses on the beginning of the comparative
... Show MoreConvert is one of the Islamic manuscript that contains an important data as the finishing date of copy , the place of copy ,the name of the copy in addition to mention converting of many data about schools,and holy places. Many copiers tried to record historical data that can not be found in other places.
Praise be to Allah the Merciful, Praise be to him what has guided us and blessed, with thanks for what Olanna, Akram, and prayed God to Muhammad, the Seal of the Prophets and The God of the good and virtuous, and to his family Almentajabin.