D(d)-VDTC猜想的反例

Journal of Jilin University Science Edition

Previous Articles Next Articles

Some Counterexamples to D(d)-VDTC Conjecture

CHEN Xiang’en, HE Yuping

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2015-06-18 Online:2016-01-26 Published:2016-01-19
Contact: CHEN Xiang’en E-mail:chenxe@nwnu.edu.cn

Abstract

Abstract:

More general counterexamples to D(d)-VDTC conjecture were obtained by means of reduction to absurdity and the method of combinatorial analysis. These examples also show that the difference between D(d)-vertex distinguishing total chromatic number and its trivial lower bound may exceed arbitrary positive integer.

Key words: total coloring, D(d)-vertex distinguishing total coloring, D(d)-vertex distinguishing total chromatic number, cycle, circulant graph

CLC Number:

O157.5

CHEN Xiang’en, HE Yuping. Some Counterexamples to D(d)-VDTC Conjecture[J].Journal of Jilin University Science Edition, 2016, 54(01): 66-69.

[1]	Wang Wenjie, Li Huichong, Wen Fei. Vertex Reducible Colorings of Generalized Petersen Graphs [J]. Journal of Jilin University Science Edition, 2026, 64(4): 789-0794.
[2]	ZHAO Qian, LI Ting. General Total Coloring of Join Graph P_m∨P_nVertex-Distinguished by Multisets [J]. Journal of Jilin University Science Edition, 2026, 64(2): 258-0264.
[3]	CHENG Lifang, LIU Xin, ZHANG Litao, CHEN Can. Dynamical Behavior of a Kind of Wing Model [J]. Journal of Jilin University Science Edition, 2026, 64(2): 430-0438.
[4]	BAI Yu, QIANG Huiying, HE Jing. D(2)-Vertex Sum Distinguishing Total Coloring of Tricyclic Graph with Non Zero Tree Height [J]. Journal of Jilin University Science Edition, 2025, 63(4): 1075-1082.
[5]	LI Weiwei, FU Bo, WANG Hefei, SUN Wenyan, XUE Yuli. Style Transfer Method of Image Ink Painting Based on Data Enhanced CycleGAN [J]. Journal of Jilin University Science Edition, 2025, 63(3): 804-0814.
[6]	HE Jing, QIANG Huiying. Bound of D(2)-Vertex Sum Distinguishing Edge-Coloring of Corona Graph of a Cycle and Simple Graphs [J]. Journal of Jilin University Science Edition, 2025, 63(2): 375-0381.
[7]	YANG Chao, CHENG Yinwan, YAO Bing. Neighbor Full Sum Distinguishing Total Coloring of 3-Regular Construction Graphs [J]. Journal of Jilin University Science Edition, 2024, 62(6): 1301-1307.
[8]	HU Huangshui, FAN Xinji, DENG Yuhuan. Improved Harris Hawk Optimization Based Clustering Protocol for Wireless Sensor Networks [J]. Journal of Jilin University Science Edition, 2024, 62(5): 1228-1234.
[9]	WANG Xuan, CHEN Xiang’en. General Total Colorings of Complete p-Partite Graphs Which Are Vertex-Distinguished by Multiple Sets [J]. Journal of Jilin University Science Edition, 2024, 62(3): 503-514.
[10]	LI Zhijun, WEN Fei. Neighbor Full Sum Distinguishing Total Coloring of Unicyclic Graph [J]. Journal of Jilin University Science Edition, 2024, 62(3): 497-502.
[11]	GUO Yaqin, CHEN Xiang’en. E-Total Coloring of Complete Bipartite Graphs K_4,n Which Are Vertex-Distinguished by Multiple Sets [J]. Journal of Jilin University Science Edition, 2024, 62(3): 480-486.
[12]	WANG Yongjun, CHEN Xiang’en. Vertex Distinguishing General Total Colorings of Complete 4-Partite Graphs K_n1,_n2,_n3,_n4by Multisets (n₁≤n₂=n₃<n₄or n₁=n₂=n₃=n₄)#br# [J]. Journal of Jilin University Science Edition, 2023, 61(5): 1037-1041.
[13]	CHENG Yinwan, YANG Chao, YAO Bing. Notes on Neighbor Sum Distinguishing Coloring of Halin Graphs [J]. Journal of Jilin University Science Edition, 2022, 60(4): 833-837.
[14]	CHEN Xiang’en, WANG Yongjun. IE-Total Coloring and General Total Coloring of Complete Bipartite Graph Which Are Vertex-Distinguished by Multiple Sets#br# [J]. Journal of Jilin University Science Edition, 2022, 60(4): 838-844.
[15]	GE Yanliang, SUN Xiaoxiao, ZHANG Qiao, WANG Dongmei, WANG Xiaoxiao. Face Sketch Synthesis Based on Cycle-Generative Adversarial Networks [J]. Journal of Jilin University Science Edition, 2022, 60(4): 897-905.

Some Counterexamples to D(d)-VDTC Conjecture

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10