Add to ORKGGiven a graph G, a function f:V(G)→ {1,2,…,k} is a k-ranking of G if f(u)=f(v) implies every u-v path contains a vertex w such that f(w)\u3ef(u). A k-ranking is minimal if the reduction of any label greater than 1 violates the described ranking property. The arank number of a graph, denoted ψr(G), is the largest k such that G has a minimal k-ranking. We present new results involving minimal k-rankings of paths. In particular, we determine ψr(Pn), a problem posed by Laskar and Pillone in 2000 (Refer to PDF file for exact formulas)
AbstractA k-edge ranking of an undirected graph is a labeling of the edges of the graph with integer...
A k-ranking of a directed graph G is a labeling of the vertex set of G with k positive integers such...
AbstractA k-ranking is a vertex k-coloring with positive integers such that if two vertices have the...
Given a graph G, a function f:V(G)→ {1,2,…,k} is a k-ranking of G if f(u)=f(v) implies every u-v pat...
AbstractGiven a graph G, a function f:V(G)→ {1,2,…,k} is a k-ranking of G if f(u)=f(v) implies every...
Given a graph G, a function f: V(G) -\u3e {1, 2, ..., k} is a k-ranking of G if f(u) = f(v) implies ...
Given a graph G, a function f: V (G) → {1, 2,..., k} is a k-ranking of G if f(u) = f(v) implies eve...
For a graph G = (V,E), a function f: V (G) → {1, 2,..., k} is a k-ranking if f(u) = f(v) implies t...
For a graph G = (V, E), a function f : V (G) → {1, 2, . . ., k} is a kranking for G if f(u) = f(v) i...
Given a graph G with a ranking function, f: V(G) --\u3e {1,2,...,k}, the ranking is minimal if only ...
A quick introduction to Graph Theory A graph, G, consists of a set of vertices,V (G), and a set of e...
AbstractA ranking of a graph is a labeling of the vertices with positive integers such that any path...
AbstractA k-ranking of a graph G is a mapping ϕ:V(G)→{1,…,k} such that any path with endvertices x a...
A k-ranking of a graph G is a colouring φ:V(G) → {1,...,k} such that any path in G with endvertices ...
summary:A $k$-ranking of a graph $G=(V,E)$ is a mapping $\varphi \:V \rightarrow \lbrace 1,2,\dots ,...
AbstractA k-edge ranking of an undirected graph is a labeling of the edges of the graph with integer...
A k-ranking of a directed graph G is a labeling of the vertex set of G with k positive integers such...
AbstractA k-ranking is a vertex k-coloring with positive integers such that if two vertices have the...
Given a graph G, a function f:V(G)→ {1,2,…,k} is a k-ranking of G if f(u)=f(v) implies every u-v pat...
AbstractGiven a graph G, a function f:V(G)→ {1,2,…,k} is a k-ranking of G if f(u)=f(v) implies every...
Given a graph G, a function f: V(G) -\u3e {1, 2, ..., k} is a k-ranking of G if f(u) = f(v) implies ...
Given a graph G, a function f: V (G) → {1, 2,..., k} is a k-ranking of G if f(u) = f(v) implies eve...
For a graph G = (V,E), a function f: V (G) → {1, 2,..., k} is a k-ranking if f(u) = f(v) implies t...
For a graph G = (V, E), a function f : V (G) → {1, 2, . . ., k} is a kranking for G if f(u) = f(v) i...
Given a graph G with a ranking function, f: V(G) --\u3e {1,2,...,k}, the ranking is minimal if only ...
A quick introduction to Graph Theory A graph, G, consists of a set of vertices,V (G), and a set of e...
AbstractA ranking of a graph is a labeling of the vertices with positive integers such that any path...
AbstractA k-ranking of a graph G is a mapping ϕ:V(G)→{1,…,k} such that any path with endvertices x a...
A k-ranking of a graph G is a colouring φ:V(G) → {1,...,k} such that any path in G with endvertices ...
summary:A $k$-ranking of a graph $G=(V,E)$ is a mapping $\varphi \:V \rightarrow \lbrace 1,2,\dots ,...
AbstractA k-edge ranking of an undirected graph is a labeling of the edges of the graph with integer...
A k-ranking of a directed graph G is a labeling of the vertex set of G with k positive integers such...
AbstractA k-ranking is a vertex k-coloring with positive integers such that if two vertices have the...