Total-Neighbor-Distinguishing Coloring by Sums of the Three Types of Product Graphs

  • Xiahong Cai
  • Shuangliang Tian
  • Huan Yang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 848)


We consider a proper total coloring \( \sigma \) of edges and vertices in a simple graph \( G \) and the sum \( f(v) \) of colors of all the edges incident to \( v \) and the color of a vertex \( v \). We say that a coloring \( \sigma \) is distinguished adjacent vertices by sums, if every two adjacent vertices have different values of \( f \), the \( \sigma \) is called total neighbor distinguishing coloring by sums. In this paper, we determine exact value of these parameters for the Cartesian product, direct product and semi strong product of infinite paths, and finite graph of the semi strong product.


Infinite path Finite graph Product graph Neighbor sum distinguishing total coloring Neighbor sum distinguishing total chromatic number 



This research was financially supported by Key Laboratory of Streaming Data Computing Technologies and Applications, State Ethnic Affairs Commission of China (No.14XBZ018) and Innovative Team Subsidize of Northwest Minzu University and Central University for Northwest Minzu University of the basic scientific research business expenses of the special funds to support graduate projects (Yxm2017103, Yxm2017105).


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Mathematics and Computer InstituteNorthwest Minzu UniverstyLanzhouChina

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