JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (4): 30-33.doi: 10.6040/j.issn.1671-9352.0.2016.242

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Vertex-distinguishing I-total colorings of the join of two paths

CHEN Xiang-en1, MIAO Ting-ting1, WANG Zhi-wen2   

  1. 1. School of Mathematics and statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. School of Mathematics and Computer Sciences, Ningxia University, Yinchuan 750021, Ningxia, China
  • Received:2016-05-26 Online:2017-04-20 Published:2017-04-11

Abstract: The problems of vertex-distinguishing I-total colorings and vertex-distinguishing VI-total colorings of the join of two paths are discussed by using the method of constructing concrete coloring. Vertex-distinguishing I-total chromatic numbers and vertex-distinguishing VI-total chromatic numbers of Pm∨Pn are determined,and the VDITC conjecture and VDVITC conjecture are valid for Pm∨Pn.

Key words: vertex distinguishing I-total coloring, vertex distinguishing I-total chromatic number, the join of graphs, I-total coloring

CLC Number: 

  • O157.5
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[1] ZHANG Fang-hong1, WANG Zhi-wen2, CHEN Xiang-en1*, YAO Bing1. Adjacent-vertex-distinguishing total chromatic numbers ofK 5∨Kt [J]. J4, 2012, 47(12): 37-40.
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