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

• Main Authors: Garciano, Agnes, Marcelo, Reginaldo M, Ruiz, Mari-Jo P, Tolentino, Mark Anthony C
• Format: text
• Published: Archīum Ateneo 2020
• Subjects: Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/123; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1122&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

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.