完全四部图Kn1,n2,n3,n4的点被多重集可区别的一般全染色(n1≤n2=n3<n4或n1=n2=n3=n4)#br#

Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (5): 1037-1041.

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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#

WANG Yongjun, CHEN Xiang’en

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

Received:2023-02-01 Online:2023-09-26 Published:2023-09-26

Abstract

Abstract: By using the method of contradiction, the method of constructing concrete coloring and distributing the color sets in advance, we discussed the general total colorings of complete 4-partite graph K_n1,_n2,_n3,_n4n₁≤n₂=n₃<n₄or n₁=n₂=n₃=n₄) that were vertex-distinguished by multisets. We gave an optimal coloring scheme and determined the chromatic numbers of the corresponding colorings.

Key words: complete 4-partite graph, general total coloring, multiset, color set, distinguishing

CLC Number:

O157.5

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.

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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#

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Vertex Distinguishing General Total Colorings of Complete 4-Partite Graphs Kn1,n2,n3,n4 by Multisets (n1≤n2=n3<n4 or n1=n2=n3=n4)#br#

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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#