A structural approach to the graceful coloring of a subclass of trees
Heliyon, ISSN: 2405-8440, Vol: 9, Issue: 9, Page: e19563
2023
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Article Description
Let M={1,2,..m} and G be a simple graph. A graceful m -coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference between their end vertices. The graceful chromatic number χg(G)= min {m:G admits a gracefulm− coloring }. We prove that 5≤χg(T)≤7, where T is a tree with Δ=4. Furthermore, we categorize the trees into three types along with its characterization and the related coloring algorithm are presented in this study.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S2405844023067713; http://dx.doi.org/10.1016/j.heliyon.2023.e19563; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85169842994&origin=inward; http://www.ncbi.nlm.nih.gov/pubmed/37809615; https://linkinghub.elsevier.com/retrieve/pii/S2405844023067713; https://dx.doi.org/10.1016/j.heliyon.2023.e19563
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