Radius-edge-invariant and diameter-edge-invariant graphs

On critical and cocritical radius edge-invariant graphs

The concepts of critical and cocritical radius edge-invariant graphs are introduced. We prove that every graph can be embedded as an induced subgraph of a critical or cocritical radius-edge-invariant graph. We show that every cocritical radius-edge-invariant graph of radius r ≥ 15 must have at least 3r + 2 vertices.

Color Invariant Edge Detection

Segmentation based on color, instead of intensity only, provides an easier distinction between materials, on the condition that robustness against irrelevant parameters is achieved, such as illumination source, shadows, geometry and camera sensitivities. Modeling the physical process of the image formation provides insight into the effect of different parameters on object color. In this paper, ...

Color Invariant Edge Dete tionJan

Diameter of paired domination edge-critical graphs

A paired dominating set of a graph G without isolated vertices is a dominating set of G whose induced subgraph has a perfect matching. The paired domination number γpr(G) of G is the minimum cardinality amongst all paired dominating sets of G. The graph G is paired domination edge-critical (γprEC) if for every e ∈ E(G), γpr(G+ e) < γpr(G). We investigate the diameter of γprEC graphs. To this ef...

Diameter vulnerability of graphs by edge deletion

Let f (t, k) be the maximum diameter of graphs obtained by deleting t edges from a (t+1)-edge-connected graph with diameter k. This paper shows 4 √ 2t−6 < f (t, 3) ≤ max{59, 5 √ 2t+7} for t ≥ 4, which corrects an improper result in [C. Peyrat, Diameter vulnerability of graphs, Discrete Appl. Math. 9 (3) (1984) 245–250] and also determines f (2, k) = 3k − 1 and f (3, k) = 4k − 2 for k ≥ 3. c © 2...