Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2021, Vol. 38 ›› Issue (5): 721-730.doi: 10.3969/j.issn.1005-3085.2021.05.011

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Neighbor Expanded Sum Distinguishing Total Colorings of Some Cartesian Product Graphs

WANG Guoxing1,2   

  1. 1. Gansu Silk Road Economic Research Institute, Lanzhou University of Finance and Economics, Lanzhou 730020
    2. College of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020
  • Online:2021-10-15 Published:2021-12-15
  • Supported by:
    The National Natural Science Foundation of China (11761064; 61662066); the Innovation Foundation of Universities in Gansu Province (2021B-148); the Key Topics of the Silk Road Economic Research Institute of Lanzhou University of Finance and Economics (JYYZ201903); the Major Bidding Project of Lanzhou University of Finance and Economics (lzufe2020a-01); the Key Research Projects of Higher Education Reform in Lanzhou University of Finance and Economics (LJZ201908).

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Abstract:

Based on the structure of Cartesian product graphs, we apply the constructional coloring functions to prove that the neighbor expanded sum distinguishing total chromatic indexes (NESDTC) of graphs $P_m\Box C_n$, $P_m\Box W_{n} (n\geq 9)$ and $P_m\Box K_n$ equal to 2. Those results show that the NESDTC-conjecture proposed by Flandrin {\sl et al} is correct for graphs $P_m\Box C_n$, $P_m\Box W_{n} (n\geq 9)$ and $P_m\Box K_n$.

Key words: $k$-total coloring, Cartesian product, neighbor expanded sum distinguishing total coloring, neighbor expanded sum distinguishing total chromatic index

CLC Number: