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Odd-Graceful Total Colorings for Constructing Graphic Lattice

Author

Listed:
  • Jing Su

    (School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China
    Key Laboratory of High Confidence Software Technologies, Peking University, Beijing 100871, China
    These authors contributed equally to this work.)

  • Hui Sun

    (School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China
    Key Laboratory of High Confidence Software Technologies, Peking University, Beijing 100871, China
    These authors contributed equally to this work.)

  • Bing Yao

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
    These authors contributed equally to this work.)

Abstract

The security of passwords generated by the graphic lattices is based on the difficulty of the graph isomorphism, graceful tree conjecture, and total coloring conjecture. A graphic lattice is generated by a graphic base and graphical operations, where a graphic base is a group of disjointed, connected graphs holding linearly independent properties. We study the existence of graphic bases with odd-graceful total colorings and show graphic lattices by vertex-overlapping and edge-joining operations; we prove that these graphic lattices are closed to the odd-graceful total coloring.

Suggested Citation

  • Jing Su & Hui Sun & Bing Yao, 2021. "Odd-Graceful Total Colorings for Constructing Graphic Lattice," Mathematics, MDPI, vol. 10(1), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:109-:d:714599
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