Title :
Kernel Set Problem and its Computation
Author :
Ge, Quanbo ; Nakata, Mitsuru
Author_Institution :
Yamaguchi Univ., Yamaguchi, Japan
Abstract :
Given with a graph G and its any isomorphic graph G´, a minimum determiner set of G is a minimum set of vertices such that, if these vertices are assigned in one-to-one correspondence between G and G´ then correspondences of the remaining vertices of G are uniquely determined. A kernel set is a minimum determiner set with the least number of elements. In this paper, we firstly define determiner set and minimum determiner set properly as well as kernel set. Then we show the related properties and propose algorithms to find minimum determiner set as a previous step toward finding kernel set. Finally, we give an example by applying proposed algorithms to show the usefulness of minimum determiner set as well as kernel set.
Keywords :
graph theory; set theory; isomorphic graph; kernel set problem; minimum determiner set; one-to-one correspondence; vertices; Kernel; Sensors; Silicon; Time complexity; Transmission line matrix methods; Vectors; correspondence; determiner set; graph; isomorphism; kernel set;
Conference_Titel :
Networking and Computing (ICNC), 2012 Third International Conference on
Conference_Location :
Okinawa
Print_ISBN :
978-1-4673-4624-5
DOI :
10.1109/ICNC.2012.74