The oriented chromatic number of Halin graphs

The locating-chromatic number for Halin graphs

Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...

Oriented chromatic number of Halin graphs

Oriented chromatic number of an oriented graph G is the minimum order of an oriented graph H such that G admits a homomorphism to H . The oriented chromatic number of an unoriented graph G is the maximal chromatic number over all possible orientations of G. In this paper, we prove that every Halin graph has oriented chromatic number at most 8, improving a previous bound by Hosseini Dolama and S...

On the oriented chromatic number of Halin graphs

An oriented k-coloring of an oriented graph G is a mapping c : V (G) → {1, 2, . . . , k} such that (i) if xy ∈ E(G) then c(x) 6= c(y) and (ii) if xy, zt ∈ E(G) then c(x) = c(t) =⇒ c(y) 6= c(z). The oriented chromatic number ~ χ(G) of an oriented graph G is defined as the smallest k such that G admits an oriented k-coloring. We prove in this paper that every Halin graph has oriented chromatic nu...

The strong chromatic index of Halin graphs

The Strong Chromatic Index of Halin Graphs By Ziyu Hu A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they have adjacent endpoints. The strong chromatic index of a graph G, denoted by χs(G), is the minimum number of colors needed for a strong edge coloring of G. A Halin graph G is a planar graph constructed...

The chromatic number of oriented graphs