منابع مشابه
A new type of edge-derived vertex coloring
We study the minimum number of weights assigned to the edges of a graph G with no component K2 so that any two adjacent vertices have distinct sets of weights on their incident edges. The best possible upper bound on this parameter is proved.
متن کاملEdge-coloring Vertex-weightings of Graphs
Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...
متن کاملVertex-coloring 2-edge-weighting of graphs
A k-edge-weighting w of a graph G is an assignment of an integer weight, w(e) ∈ {1, . . . , k}, to each edge e. An edge weighting naturally induces a vertex coloring c by defining c(u) = ∑ u∼e w(e) for every u ∈ V (G). A k-edge-weighting of a graph G is vertexcoloring if the induced coloring c is proper, i.e., c(u) ≠ c(v) for any edge uv ∈ E(G). Given a graph G and a vertex coloring c0, does th...
متن کاملVertex-coloring edge-weightings of graphs
A k-edge-weighting of a graph G is a mapping w : E(G) → {1, 2, . . . , k}. An edgeweighting w induces a vertex coloring fw : V (G) → N defined by fw(v) = ∑ v∈e w(e). An edge-weighting w is vertex-coloring if fw(u) 6= fw(v) for any edge uv. The current paper studies the parameter μ(G), which is the minimum k for which G has a vertexcoloring k-edge-weighting. Exact values of μ(G) are determined f...
متن کاملAdjacent vertex-distinguishing edge coloring of graphs
An adjacent vertex-distinguishing edge coloring, or avd-coloring, of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let mad(G) and ∆(G) denote the maximum average degree and the maximum degree of a graph G, respectively. In this paper, we prove that every graph G with ∆(G) ≥ 5 and mad(G) < 3− 2 ∆ can be avd-colored with ∆(G) + 1 col...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.11.014