Rainbow connection numbers of Cartesian product of graphs

Rainbow connection numbers of Cartesian product of graphs Yu-Jung Liang Department of Applied Mathematics National Dong Hwa University Advisor: Professor David Kuo

Outline �Introduction �Previous Results �Main Results

Definition (The Cartesian product) �

Definition (Rainbow connection number) �

� 2 5 2 1 1 3 3 2 1 2 4 3 5 5 4 2 1 4 1 3 3 2 1 2 1

Previous Results � back 1

� back

Main Results �Particular labeling 0 0 1 1 2 3 1 4 3 2 0 1 2 3 0 1 0 3 2 1 2 4 0 3

Rainbow connection numbers of the Cartesian product of paths and cycles �

� 3 2 1 1 3 2 1 2 2 1 1 3 3 2 1 1 3 2 1 3 Thm 1

Rainbow connection numbers of the Cartesian product of two trees �

� 1 1 2 2 3 3 1 3 Thm 3

� 7 1 2 3 3 1 2 4 4 5 6 6

7 4 5 6 6 4 5 1 1 2 3 3

� 7 4 4 7 7 5 8 5 7 8 6 6 1 1 8 2 8 8 4 3 8 8 2 5 8 3 3 8 6

� 7 1 1 2 3 1 4 2 2 3 8 3 4 5 3 6 5 6 6

7 4 4 5 6 4 1 5 5 6 8 6 1 2 6 3 2 3 3

� 7 4 5 2 3 9 9 1 9 9 5 7 7 8 4 1 1 1 8 9 7 5 6 6 4 8 9 6 9 9 9 2 3 6 4 9 9 2 3 9 9 6 9 5 3 9 2 9 6 3

� 1 2 1 3 2 3 1

� 2 3 2 1 2 3 1 2 1 3 1 2 3 1 3 2 2 3 3 1 2 3 1 1