The sigma chromatic number of the Sierpinski gasket graphs and the Hanoi graphs

Authors

Agnes Garciano, Ateneo de Manila UniversityFollow
Reginaldo M. Marcelo, Ateneo de Manila UniversityFollow
Mari-Jo P. Ruiz, Ateneo de Manila UniversityFollow
Mark Anthony C. Tolentino, Ateneo de Manila UniversityFollow

Document Type

Article

Publication Date

2020

Abstract

A vertex coloring c : V(G) → of a non-trivial connected graph G is called a sigma coloring if σ(u) ≠ σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we determine the sigma chromatic numbers of the Sierpiński gasket graphs and the Hanoi graphs. Moreover, we prove the uniqueness of the sigma coloring for Sierpiński gasket graphs.

Recommended Citation

Garciano, A. D., Marcelo, R. M., Ruiz, M. J. P., & Tolentino, M. A. C. (2020, May). The sigma chromatic number of the Sierpiński gasket graphs and the Hanoi graphs. In Journal of Physics: Conference Series (Vol. 1538, No. 1, p. 012002). IOP Publishing.