Graphs with multiplicative vertex-coloring 2-edge-weightings
نویسندگان
چکیده
منابع مشابه
Edge-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 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 کاملVertex-coloring edge-weightings: Towards the 1-2-3-conjecture
A weighting of the edges of a graph is called vertexcoloring if the weighted degrees of the vertices yield a proper coloring of the graph. In this paper we show that such a weighting is possible from the weight set {1, 2, 3, 4, 5} for all graphs not containing components with exactly 2 vertices. All graphs in this note are finite and simple. For notation not defined here we refer the reader to ...
متن کاملVertex Coloring of Graphs by Total 2-Weightings
An assignment of real weights to the edges and the vertices of a graph is a vertexcoloring total weighting if the total weight sums at the vertices are distinct for any two adjacent vertices. Of interest in this paper is the existence of vertex-coloring total weightings with weight set of cardinality two, a problem motivated by the conjecture that every graph has a such a weighting using the we...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2015
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-015-9966-7