On the Sigma Value and Sigma Range of the Join of a Finite Number of Even Cycles of the Same Order

• Main Authors: Bulay-og, Marie Cris A, Garciano, Agnes, Marcelo, Reginaldo M
• Format: text
• Published: Archīum Ateneo 2021
• Subjects: sigma coloring of a graph; sigma value; sigma range; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/159; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1166&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

Let c be a vertex coloring of a simple; connected graph G that uses positive integers for colors. For a vertex v of G; the color sum of v is the sum of the colors of the neighbors of v. If no two adjacent vertices of G have the same color sum; then c is called a sigma coloring of G. The sigma chromatic number of G is the minimum number of colors required in a sigma coloring of G. Let max(c) be the largest color assigned to a vertex of G by a coloring c. The sigma value of G is the minimum value of max(c) over all sigma k−colorings c of G where k is the sigma chromatic number of G. On the other hand; the sigma range of G is the minimum value of max(c) over all sigma colorings c of G. In this paper; we determine the sigma value and the sigma range of the join of a finite number of even cycles of the same order.