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Color Energy Of A Unitary Cayley Graph

Chandrashekar Adiga;  E. Sampathkumar;  M.A. Sriraj — 2014

Discussiones Mathematicae Graph Theory

Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G) and computed the color energy of few families of graphs with χ(G) colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xn)c and some gcd-graphs.

3-consecutive c-colorings of graphs

Csilla Bujtás;  E. Sampathkumar;  Zsolt Tuza;  M.S. Subramanya;  Charles Dominic — 2010

Discussiones Mathematicae Graph Theory

A 3-consecutive C-coloring of a graph G = (V,E) is a mapping φ:V → ℕ such that every path on three vertices has at most two colors. We prove general estimates on the maximum number ( χ ̅ ) 3 C C ( G ) of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with ( χ ̅ ) 3 C C ( G ) ≥ k for k = 3 and k = 4.

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