完全二部图K_(10,n)(91≤n≤214)的点可区别E-全染色
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摘要
令χvet(G)=min{k|G存在k-VDET染色},称χvet(G)为图G的点可区别E-全色数.运用分析法和反证法,讨论并给出了完全二部图K10, n(91≤n≤214)的点可区别E-全色数.
Let χvet(G)= min{k|G has a k-VDET coloring}, then χvet(G) is called the VDET chromatic number of G. By using the analytical method and proof via contradiction, the VDET coloring of complete bipartite graph K10, nwas discussed and the VDET chromatic number of K10, n(91≤ n ≤ 214) had been obtained.
Let χvet(G)= min{k|G has a k-VDET coloring}, then χvet(G) is called the VDET chromatic number of G. By using the analytical method and proof via contradiction, the VDET coloring of complete bipartite graph K10, nwas discussed and the VDET chromatic number of K10, n(91≤ n ≤ 214) had been obtained.
引文
[1]陈祥恩,高毓平.合成图的点可区别正常边色数[J].吉林大学学报:理学版, 2011, 49(2):207-212.
[2]杨芳,王治文,陈祥恩,等.完全图和星的合成的点可区别正常边染色[J].华东师范大学学报:自然科学版,2013, 2013(5):136-143.
[3] Zhang Zhong-fu, Qiu Peng-xiang, Li Jing-wen, et al. Vertex distinguishing total colorings of graphs[J]. Ars Combinatoria, 2008, 87:33-45.
[4] Chen Xiang-en, Gao Yu-ping, Yao Bing. Relations of vertex distinguishing total chromatic numbers between a subgraph and its supergraph[J]. Information Sciences,2014, 288:246-253
[5]辛小青,王治文,陈祥恩,等.点不交的m个C3的并的点可区别全染色[J].吉林大学学报:理学版, 2012, 50(2):251-257.
[6]辛小青,陈祥恩. m个点不交的C4的并的点可区别全染色[J].山东大学学报:理学版, 2010, 45(10):35-39.
[7]马彦荣,王治文,陈祥恩,等. mK2, 3的点可区别全染色[J].西南大学学报:自然科学版, 2011, 33(6):115-120.
[8]陈祥恩,王治文,马彦荣,等. mK4的点可区别全染色[J].吉林大学学报:理学版, 2012, 50(4):686-692.
[9]何玉萍,王治文,陈祥恩. mC8的点可区别全染色[J].山东大学学报:理学版, 2017, 52(10):24-30.
[10]何玉萍,王治文,陈祥恩. mC7的点可区别全染色[J].吉林大学学报:理学版, 2017, 55(3):531-536.
[11]何玉萍,王治文,陈祥恩. mC3的点可区别全染色[J].中山大学学报:自然科学版, 2018, 57(1):69-75.
[12]陈祥恩,李婷,王治文.一类含有4-圈的单圈图一般点可区别全染色[J].大连理工大学学报, 2017, 57(3):316-320.
[13]陈祥恩,苏丽,王治文.完全二部图K2, n, K3, n的一般点可区别全染色[J].吉林大学学报:理学版, 2016, 54(6):1289-1293.
[14] Chen Xiang-en, Zu Yue, Zhang Zhong-fu. Vertex-distinguishing E-total colorings of graphs[J]. Arabian Journal for Science and Engineering, 2011, 36(8):1485-1500.
[15] Chen Xiang-en, Zu Yue. Vertex-distinguishing E-total coloring of the graphs mC3and mC4[J]. Journal of Mathematical Research&Exposition, 2011, 31:45-58.
[16]李世玲,陈祥恩,王治文.完全二部图K3, n(3≤n≤17)的点可区别E-全染色[J].吉林大学学报:理学版, 2015,53(6):1171-1176.
[17]李世玲,陈祥恩,王治文.完全二部图K3, n(n≥18)的点可区别E-全染色[J].山东大学学报:理学版, 2015,51(4):68-71.
[18]李世玲.完全二部图的点可区别E-全染色的若干结果[D].兰州:西北师范大学数学与统计学院, 2017.
[19] Chen Xiang-en. Vertex-distinguishing E-total coloring of complete bipartite graph K7, nwhen 7≤n≤95[J]. Communications in Mathematical Research, 2016, 32(4):359-374.
[20]包丽娅,陈祥恩,王志文.完全二部图K10, n(10≤n≤90)的点可区别E-全染色[J].山东大学学报:理学版,2018, 53(12):23-30.
[2]杨芳,王治文,陈祥恩,等.完全图和星的合成的点可区别正常边染色[J].华东师范大学学报:自然科学版,2013, 2013(5):136-143.
[3] Zhang Zhong-fu, Qiu Peng-xiang, Li Jing-wen, et al. Vertex distinguishing total colorings of graphs[J]. Ars Combinatoria, 2008, 87:33-45.
[4] Chen Xiang-en, Gao Yu-ping, Yao Bing. Relations of vertex distinguishing total chromatic numbers between a subgraph and its supergraph[J]. Information Sciences,2014, 288:246-253
[5]辛小青,王治文,陈祥恩,等.点不交的m个C3的并的点可区别全染色[J].吉林大学学报:理学版, 2012, 50(2):251-257.
[6]辛小青,陈祥恩. m个点不交的C4的并的点可区别全染色[J].山东大学学报:理学版, 2010, 45(10):35-39.
[7]马彦荣,王治文,陈祥恩,等. mK2, 3的点可区别全染色[J].西南大学学报:自然科学版, 2011, 33(6):115-120.
[8]陈祥恩,王治文,马彦荣,等. mK4的点可区别全染色[J].吉林大学学报:理学版, 2012, 50(4):686-692.
[9]何玉萍,王治文,陈祥恩. mC8的点可区别全染色[J].山东大学学报:理学版, 2017, 52(10):24-30.
[10]何玉萍,王治文,陈祥恩. mC7的点可区别全染色[J].吉林大学学报:理学版, 2017, 55(3):531-536.
[11]何玉萍,王治文,陈祥恩. mC3的点可区别全染色[J].中山大学学报:自然科学版, 2018, 57(1):69-75.
[12]陈祥恩,李婷,王治文.一类含有4-圈的单圈图一般点可区别全染色[J].大连理工大学学报, 2017, 57(3):316-320.
[13]陈祥恩,苏丽,王治文.完全二部图K2, n, K3, n的一般点可区别全染色[J].吉林大学学报:理学版, 2016, 54(6):1289-1293.
[14] Chen Xiang-en, Zu Yue, Zhang Zhong-fu. Vertex-distinguishing E-total colorings of graphs[J]. Arabian Journal for Science and Engineering, 2011, 36(8):1485-1500.
[15] Chen Xiang-en, Zu Yue. Vertex-distinguishing E-total coloring of the graphs mC3and mC4[J]. Journal of Mathematical Research&Exposition, 2011, 31:45-58.
[16]李世玲,陈祥恩,王治文.完全二部图K3, n(3≤n≤17)的点可区别E-全染色[J].吉林大学学报:理学版, 2015,53(6):1171-1176.
[17]李世玲,陈祥恩,王治文.完全二部图K3, n(n≥18)的点可区别E-全染色[J].山东大学学报:理学版, 2015,51(4):68-71.
[18]李世玲.完全二部图的点可区别E-全染色的若干结果[D].兰州:西北师范大学数学与统计学院, 2017.
[19] Chen Xiang-en. Vertex-distinguishing E-total coloring of complete bipartite graph K7, nwhen 7≤n≤95[J]. Communications in Mathematical Research, 2016, 32(4):359-374.
[20]包丽娅,陈祥恩,王志文.完全二部图K10, n(10≤n≤90)的点可区别E-全染色[J].山东大学学报:理学版,2018, 53(12):23-30.