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

Previous Articles     Next Articles

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

PDF (PC)

485

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
[1] BURRIS A C, SCHELP R H. Vertex-distinguish proper edge-colorings[J]. J Graph Theory, 1997, 26(2):73-82.
[2] BAZGAN C, HARKAT-BENHANDINE A, LI Hao, et al. On the vertex-distinguish proper edge-colorings of graphs[J]. J of Comb Theory: Series B, 1999, 75(2):288-301.
[3] HARARY F, PLANTHOLT M. The point-distinguishing chromatic index[M] // HARARY F, MAYBEE J S. Graphs and Application. New York: Wiley Interscience, 1985: 147-162.
[4] CHEN Xiangen. Point-distinguishing chromatic index of the union of paths[J]. Czechoslovak Mathematical Journal, 2014, 64(3):629-640.
[5] ZHANG Zhongfu, QIU Pengxiang, XU Baogen, et al. Vertex-distinguishing total colorings of graphs[J]. Ars Combinatoria, 2008, 87:33-45.
[6] CHEN Xiangen, LI Zepeng. Vertex-distinguishing I-total colorings of graphs[J]. Utilitas Mathematica, 2014, 95:319-327.
[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.
[2] CHENG Hui, WANG Zhi-yong. The adjacent vertex strongly distinguishing EI-total colorings of graphs [J]. J4, 2010, 45(6): 18-22.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd