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...
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Let G be a graph and A an Abelian group. Denote by F (G,A) the set of all functions from E(G) to A. Denote by D an orientation of E(G). For f ∈ F (G,A), an (A, f)-coloring of G under the orientation D is a function c : V (G) 7→ A such that for every directed edge uv from u to v, c(u) − c(v) 6= f(uv). G is A-colorable under the orientation D if for any function f ∈ F (G,A), G has an (A, f)-color...
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Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
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For a coloring $c$ of a graph $G$, the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively $sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$, where the summations are taken over all edges $abin E(G)$. The edge-difference chromatic sum, denoted by $sum D(G)$, and the edge-sum chromatic sum, denoted by $sum S(G)$, a...
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Let G be a graph with a ®xed orientation and let A be a group. Let F G; A denote the set of all functions f : E G U 3 A. The graph G is A-colorable if for any function f P F G; A, there is a function c: V G U 3 A such that for every directed e uv P E G, c u À c v T f e. The group chromatic number v 1 G of a graph G is the minimum m such that G is A-colorable for any group A of...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2016
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2016.02.002