Title :
The Nonlinear matrix Equation Xm = A and its Applications to Graph Theory
Author :
Yuan-Yuan Li ; Yu Li
Author_Institution :
Sch. of Math. & Comput. Sci., Jiang-Han Univ., Wuhan
Abstract :
Nonlinear matrix equation widely used in the control theory.When restricted to integer rings ,the integer matrix and the finite directed graph is corresponding.This paper made the integer root of matrix equation applied to the graph theory, and get several propositions about existence of the underlying graph(root graph) of special graphs. And we obtained the algebraic approach on how to find the adjacency matrix of the underlying graph(root graph). Finally, we also determine the precise number of solutions in various cases.
Keywords :
directed graphs; integer programming; matrix algebra; nonlinear equations; finite directed graph; graph theory; integer matrix; nonlinear matrix equation; root graph; Codes; Control theory; Educational institutions; Graph theory; Mathematics; Matrices; Nonlinear equations;
Conference_Titel :
Innovative Computing Information and Control, 2008. ICICIC '08. 3rd International Conference on
Conference_Location :
Dalian, Liaoning
Print_ISBN :
978-0-7695-3161-8
Electronic_ISBN :
978-0-7695-3161-8
DOI :
10.1109/ICICIC.2008.565