Contraction-criticality for the domination number of graphs and application for Vizing's conjecture
Project/Area Number |
26800086
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
|
Research Institution | Kitasato University (2016-2017) Tokyo University of Science (2014-2015) |
Principal Investigator |
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | グラフ理論 / 支配数 / Vizing予想 / 臨界的グラフ / 多彩支配数 / 直径 / 最大次数 / 縮約臨界的グラフ / 臨界頂点 / Nordhaus-Gaddum型不等式 |
Outline of Final Research Achievements |
In this research, we focused on the graphs having the domination-criticality for the contraction or addition of edges, or the deletion of vertices, and gave some generalizations for such concepts. By using such new concept, we generalized some theorems concerning upper bounds on the diameter of vertex-deletion critical graphs. Furthermore, we also gave a sufficient condition forcing the rainbow domination of graphs to be trivial value via maximum degree. So we can see when the rainbow domination number is appropriate to be used for a generalization of the domination number.
|
Report
(5 results)
Research Products
(33 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Journal Article] The k-rainbow reinforcement numbers in graphs2017
Author(s)
Jafar Amjadi, Leila Asgharsharghi, Nasrin Dehgardi, Michitaka Furuya, Seyed M. Sheikholeslami, Lutz Volkmann
-
Journal Title
Discrete Applied Mathematics
Volume: 340
Pages: 1419-1425
DOI
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-