Rainbow Graphs and Switching Classes
نویسندگان
چکیده
A rainbow graph is a graph that admits a vertex-coloring such that every color appears exactly once in the neighborhood of each vertex. We investigate some properties of rainbow graphs. In particular, we show that there is a bijection between the isomorphism classes of n-rainbow graphs on 2n vertices and the switching classes of graphs on n vertices.
منابع مشابه
Total $k$-Rainbow domination numbers in graphs
Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...
متن کاملComplexity of Rainbow Vertex Connectivity Problems for Restricted Graph Classes
A path in a vertex-colored graph G is vertex rainbow if all of its internal vertices have a distinct color. The graph G is said to be rainbow vertex connected if there is a vertex rainbow path between every pair of its vertices. Similarly, the graph G is strongly rainbow vertex connected if there is a shortest path which is vertex rainbow between every pair of its vertices. We consider the comp...
متن کاملRainbow Domination and Related Problems on Some Classes of Perfect Graphs
Let k ∈ N and let G be a graph. A function f : V (G) → 2 is a rainbow function if, for every vertex x with f(x) = ∅, f(N(x)) = [k]. The rainbow domination number γkr(G) is the minimum of ∑ x∈V (G) |f(x)| over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs.
متن کاملProgress on Rainbow Connection
An edge-coloured graph G is called rainbow-connected if any two vertices are connected by a path whose edges have different colours. This concept of rainbow connection in graphs was recently introduced by Chartrand et al. in [4]. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. An easy ob...
متن کاملOn the 2-rainbow domination in graphs
The concept of 2-rainbow domination of a graph G coincides with the ordinary domination of the prism G K2. In this paper, we show that the problem of deciding if a graph has a 2-rainbow dominating function of a given weight is NP-complete even when restricted to bipartite graphs or chordal graphs. Exact values of 2-rainbow domination numbers of several classes of graphs are found, and it is sho...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 27 شماره
صفحات -
تاریخ انتشار 2013