Let G be a (multi)graph of order n and let u,v vertices G. The maximum number internally disjoint u–v paths in is denoted by κG(u,v), the edge-disjoint λG(u,v). average connectivity defined κ¯(G)=∑κG(u,v)∕n2, edge-connectivity λ¯(G)=∑λG(u,v)∕n2, where both sums run over all unordered pairs {u,v}⊆V(G). A graph called ideally connected if κG(u,v)=min{deg(u),deg(v)} for {u,v} We prove that every m...

Halfedge data structures (HDS) are fundamental in representing combinatorial geometric structures, useful for representing any planar structures such as plane graphs and planar maps, polyhedral surfaces and boundary representations (BREPs), two-dimensional views of a three dimensional scene, etc. Many variants have been proposed in the literature, starting with the winged-edge data structure of...

We study the unitary Cayley graph associated to an arbitrary finite ring, determining precisely its diameter, girth, eigenvalues, vertex and edge connectivity, and vertex and edge chromatic number. We also compute its automorphism group, settling a question of Klotz and Sander. In addition, we classify all planar graphs and perfect graphs within this class.

This paper proposes an algorithm for detecting artificial text in video frames using edge information. First, an edge map is created using the Canny edge detector. Then, morphological dilation and opening are used in order to connect the vertical edges and eliminate false alarms. Bounding boxes are determined for every non-zero valued connected component, consisting the initial candidate text a...

A multigraph is exactly k-edge-connected if there are exactly k edgedisjoint paths between any pair of vertices. We characterize the class of exactly 3-edge-connected graphs, giving a synthesis involving two operations by which every exactly 3-edge-connected multigraph can be generated. Slightly modi ed syntheses give the planar exactly 3-edge-connected graphs and the exactly 3-edge-connected g...

The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split...

Let G 1⁄4 ðV ;EÞ be a k-regular graph with connectivity j and edge connectivity k. G is maximum connected if j 1⁄4 k, and G is maximum edge connected if k 1⁄4 k. Moreover, G is super-connected if it is a complete graph, or it is maximum connected and every minimum vertex cut is fxjðv; xÞ 2 Eg for some vertex v 2 V ; and G is super-edge-connected if it is maximum edge connected and every minimum...

Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai [Z.-H. Chen, H.-J. Lai, Reduction techniques for super-Eulerian graphs and related topics— an update, in: Ku Tung-Hsin (Ed.), Combinatorics and Graph Theory, vol. 95, World Scientific, Singapore/London, 1995, pp. 53–69, Conjecture 8.6] conjectured that every 3-edge connected, essentially 6-edge connected graph ...

the analysis of vulnerability in networks generally involves some questions about how the underlying graph is connected. one is naturally interested in studying the types of disruption in the network that maybe caused by failures of certain links or nodes. in terms of a graph, the concept of connectedness is used in dierent forms to study many of the measures of vulnerability. when certain ver...