منابع مشابه
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...
متن کاملOriented 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...
متن کاملOn 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...
متن کاملBoxicity of Halin graphs
A k-dimensional box is the Cartesian product R1 × R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such ...
متن کاملLinear Arrangement of Halin Graphs
We study the Optimal Linear Arrangement (OLA) problem of Halin graphs, one of the simplest classes of non-outerplanar graphs. We present several properties of OLA of general Halin graphs. We prove a lower bound on the cost of OLA of any Halin graph, and define classes of Halin graphs for which the cost of OLA matches this lower bound. We show for these classes of Halin graphs, OLA can be comput...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1988
ISSN: 0166-218X
DOI: 10.1016/0166-218x(88)90126-6