Abstract
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.
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Acknowledgments
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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Cai, X., Tian, S., Yang, H. (2018). Total-Neighbor-Distinguishing Coloring by Sums of the Three Types of Product Graphs. In: Yuan, H., Geng, J., Liu, C., Bian, F., Surapunt, T. (eds) Geo-Spatial Knowledge and Intelligence. GSKI 2017. Communications in Computer and Information Science, vol 848. Springer, Singapore. https://doi.org/10.1007/978-981-13-0893-2_23
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DOI: https://doi.org/10.1007/978-981-13-0893-2_23
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