Total-Neighbor-Distinguishing Coloring by Sums of the Three Types of Product Graphs
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.
KeywordsInfinite 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).
- 15.Su, Z., Wang, T., Hamdi, M.: COSTA: cross-layer optimization for sketch-based software defined measurement task assignment. In: IEEE/ACM International Symposium on Quality and Service (IWQoS 2015) (2015)Google Scholar