Search results for "Graph bandwidth"
showing 3 items of 3 documents
Multilevel Bandwidth and Radio Labelings of Graphs
2008
This paper introduces a generalization of the graph bandwidth parameter: for a graph G and an integer k ≤ diam(G), the k-level bandwidth Bk(G)of G is defined by Bk(G) = minγ max{|γ(x)-γ(y)|-d(x, y)+1 : x, y ∈ V (G), d(x, y) ≤ k}, the minimum being taken among all proper numberings γ of the vertices of G. We present general bounds on Bk(G) along with more specific results for k = 2 and the exact value for k = diam(G). We also exhibit relations between the k-level bandwidth and radio k-labelings of graphs from which we derive a upper bound for the radio number of an arbitrary graph.
Distance graphs and the T-coloring problem
1999
Abstract The T-coloring problem is, given a graph G = (V, E), a set T of nonnegative integers containing 0, and a ‘span’ bound s ⩾ 0, to compute an integer coloring f of the vertices of G such that |f(ν) − f(w)| ∉ T ∀νw ∈ E and max f − min f ⩽ s. This problem arises in the planning of channel assignments for broadcast networks. When restricted to complete graphs, the T-coloring problem boils down to a number problem which can be solved efficiently for many types of sets T. The paper presents results indicating that this is not the case if the set T is arbitrary. To these ends, the class of distance graphs is introduced, which consists of all graphs G : G ≅ G(A) for some (finite) set of posi…
Graph-based minimal path tracking in the skeleton of the retinal vascular network
2012
This paper presents a semi-automatic framework for minimal path tracking in the skeleton of the retinal vascular network. The method is based on the graph structure of the vessel network. The vascular network is represented based on the skeleton of the available segmented vessels and using an undirected graph. Significant points on the skeleton are considered nodes of the graph, while the edge of the graph is represented by the vessel segment linking two neighboring nodes. The graph is represented then in the form of a connectivity matrix, using a novel method for defining vertex connectivity. Dijkstra and Floyd-Warshall algorithms are applied for detection of minimal paths within the graph…