Studies on generation of graph classes with self-similar stuructures and investigation of their structural properties with applications

2016 Fiscal Year Final Research Report

• Project/Area Number: 25330015
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: The University of Tokushima
• Principal Investigator: Hasunuma Toru 徳島大学, 大学院理工学研究部, 准教授 (30313406)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: グラフ理論 / 細分線グラフ演算 / シェルピンスキーグラフ / 完全独立全域木 / 連結防衛同盟 / 連結支配集合 / 相互結合網 / 耐故障性

Outline of Final Research Achievements

We have newly introduced the subdivided-line graph operation and defined the class of iterated subdivided-line graphs which essentially contains well-known graph classes with self-similar structures such as the Sierpinski graphs and the extended Sierpinski graphs. We have then studied their structural properties such as edge-disjoint Hamilton cycles, hamiltonian-connectivity, hub sets, connected dominating sets, independent spanning trees, completely independent spanning trees, various colorings and labelings, globally h-connected defensive t-alliances, and (h,l)-connected dominating sets. We have also shown results on structural properties for base graphs of injective graph expansions. Moreover, we have newly introduced the class of universalized Sierpinski graphs which contains both the classes of generalized Sierpinski graphs and extended Sierpinski graphs, and then studied their structural properties which can be applied to fault-tolerant problems on interconnection networks.

Free Research Field

情報学基礎理論