Journal of Jilin University Science Edition ›› 2024, Vol. 62 ›› Issue (1): 1-0006.

    Next Articles

D(2)-Vertex-Distinguishing Total Colorings of a Class of Cactus Graphs

WANG Yinfang1, LI Muchun1, WANG Guoxing2   

  1. 1. Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China;
    2. School of Information Science and Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, China
  • Received:2023-04-14 Online:2024-01-26 Published:2024-01-26

Abstract: By applying mathematics induction and combinatorial analysis, we gave D(2)-vertex-distinguishing total colorings of cactus graphs GT with maximum degree of 3, and then obtained χ2vt(GT)≤6. The result shows that D(β)-VDTC conjecture holds for cactus graphs with maximum degree of 3.

Key words: cactus graph, D(2)-vertex-distinguishing total cocoring, D(2)-vertex-distinguishing total chromatic number

CLC Number: 

  • O157.5