Graphs in Network Flows

Vector Flows in Graphs and Integer Flows in Signed Graphs

My research focuses on the flow problems consisting of two parts, vector flows in graphs and integer flows in signed graphs. The concept of integer flows was first introduced by Tutte (1949) as a refinement of map coloring. In fact, integer flows is the dual concept of map coloring for planar graphs. This is often referred as duality theorem. Tutte proposed three celebrated flow conjectures whi...

On flows in bidirected graphs

Bouchet conjectured that every bidirected graph which admits a nowhere-zero bidirected flow will admit a nowhere-zero bidirected 6-flow [A. Bouchet, Nowhere-zero integer flows on a bidirected graph, J. Combin. Theory Ser. B 34 (1983) 279–292]. He proved that this conjecture is true with 6 replaced by 216. Zyka proved in his Ph.D dissertation that it is true with 6 replaced by 30. Khelladi prove...

analysis of power in the network society

اندیشمندان و صاحب نظران علوم اجتماعی بر این باورند که مرحله تازه ای در تاریخ جوامع بشری اغاز شده است. ویژگیهای این جامعه نو را می توان پدیده هایی از جمله اقتصاد اطلاعاتی جهانی ، هندسه متغیر شبکه ای، فرهنگ مجاز واقعی ، توسعه حیرت انگیز فناوری های دیجیتال، خدمات پیوسته و نیز فشردگی زمان و مکان برشمرد. از سوی دیگر قدرت به عنوان موضوع اصلی علم سیاست جایگاه مهمی در روابط انسانی دارد، قدرت و بازتولید...

Flows and Colorings of Graphs

On Circular Flows Of Graphs

A sufficient condition for graphs with circular flow index less than 4 is found in this paper. In particular, we give a simple proof of a result obtained by Galluccio and Goddyn (Combinatorica, 2002), and obtain a larger family of such graphs. We refer readers to [1], [2] and [7] for the standard terminology and notations in this paper. The following theorem was proved by Galluccio and Goddyn. ...