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Some useful inequalities via trace function method in Euclidean Jordan algebras
Adjacent vertex distinguishing edge-colorings and total-colorings of the Cartesian product of graphs
1. | College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, China, China, China |
2. | College of Management, Northwest University for Nationalities, Lanzhou 730030, China |
References:
[1] |
S. Akbari, H. Bidkhori and N. Nosrati, r-Strong edge colorings of graphs, Discrete Math., 306 (2006), 3005-3010.
doi: 10.1016/j.disc.2004.12.027. |
[2] |
P. N. Balister, E. Győri, J. Lehel and R. H. Schelp, Adjacent vertex distinguishing edge-colorings, SIAM J. Discrete Math., 21 (2007), 237-250.
doi: 10.1137/S0895480102414107. |
[3] |
J-L. Baril, H. Kheddouci and O. Togni, Adjacent vertex distinguishing edge-colorings of meshes, Australasian Journal of Combinatorics, 35 (2006), 89-102. |
[4] |
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier, New York, 1976. |
[5] |
M. Chen and X. Guo, Adjacent vertex-distinguishing edge and total chromatic numbers of hypercubes, Information Processing Letters, 109 (2009), 599-602.
doi: 10.1016/j.ipl.2009.02.006. |
[6] |
K. Edwards, M. Horňák and M. Woźniak, On the neighbor-distinguishing index of a graph, Graphs Combin., 22 (2006), 341-350.
doi: 10.1007/s00373-006-0671-2. |
[7] |
H. Hatami, ∆+300 is a bound on the adjacent vertex distinguishing edge chromatic number, J. Combin. Theory Ser. B, 95 (2005), 246-256.
doi: 10.1016/j.jctb.2005.04.002. |
[8] |
S. Tian and P. Chen, On adjacent vertex-distinguishing total coloring of two classes of product graphs, Journal of Mathematical Research and Exposition, 27 (2007), 733-737. |
[9] |
H. Wang, On the adjacent vertex-distinguishing total chromatic numbers of the graphs with ∆(G)=3, Journal of Combinatorial Optimization, 14 (2007), 87-109.
doi: 10.1007/s10878-006-9038-0. |
[10] |
H. P. Yap, Total Coloring of Graph, Springer Verlag, New York, 1996. |
[11] |
Z. Zhang, X. Chen, J. Li, B. Yao, X. Lu and J. Wang, On adjacent-vertex-distinguishing total coloring of graphs, Science in China Series A, Mathematics, 48 (2005), 289-299.
doi: 10.1360/03YS0207. |
[12] |
Z. Zhang, L. Liu and J. Wang, Adjacent strong edge coloring of graphs, Applied Mathematics Letters, 15 (2002), 623-626.
doi: 10.1016/S0893-9659(02)80015-5. |
show all references
References:
[1] |
S. Akbari, H. Bidkhori and N. Nosrati, r-Strong edge colorings of graphs, Discrete Math., 306 (2006), 3005-3010.
doi: 10.1016/j.disc.2004.12.027. |
[2] |
P. N. Balister, E. Győri, J. Lehel and R. H. Schelp, Adjacent vertex distinguishing edge-colorings, SIAM J. Discrete Math., 21 (2007), 237-250.
doi: 10.1137/S0895480102414107. |
[3] |
J-L. Baril, H. Kheddouci and O. Togni, Adjacent vertex distinguishing edge-colorings of meshes, Australasian Journal of Combinatorics, 35 (2006), 89-102. |
[4] |
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier, New York, 1976. |
[5] |
M. Chen and X. Guo, Adjacent vertex-distinguishing edge and total chromatic numbers of hypercubes, Information Processing Letters, 109 (2009), 599-602.
doi: 10.1016/j.ipl.2009.02.006. |
[6] |
K. Edwards, M. Horňák and M. Woźniak, On the neighbor-distinguishing index of a graph, Graphs Combin., 22 (2006), 341-350.
doi: 10.1007/s00373-006-0671-2. |
[7] |
H. Hatami, ∆+300 is a bound on the adjacent vertex distinguishing edge chromatic number, J. Combin. Theory Ser. B, 95 (2005), 246-256.
doi: 10.1016/j.jctb.2005.04.002. |
[8] |
S. Tian and P. Chen, On adjacent vertex-distinguishing total coloring of two classes of product graphs, Journal of Mathematical Research and Exposition, 27 (2007), 733-737. |
[9] |
H. Wang, On the adjacent vertex-distinguishing total chromatic numbers of the graphs with ∆(G)=3, Journal of Combinatorial Optimization, 14 (2007), 87-109.
doi: 10.1007/s10878-006-9038-0. |
[10] |
H. P. Yap, Total Coloring of Graph, Springer Verlag, New York, 1996. |
[11] |
Z. Zhang, X. Chen, J. Li, B. Yao, X. Lu and J. Wang, On adjacent-vertex-distinguishing total coloring of graphs, Science in China Series A, Mathematics, 48 (2005), 289-299.
doi: 10.1360/03YS0207. |
[12] |
Z. Zhang, L. Liu and J. Wang, Adjacent strong edge coloring of graphs, Applied Mathematics Letters, 15 (2002), 623-626.
doi: 10.1016/S0893-9659(02)80015-5. |
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