This paper addresses the problem of super resolution obtaining a single high-resolution image given a set of low resolution images which are related by small displacements. We employ reconstruction based approach using MRF-MAP formalism, and use approximate optimization using graph cuts to carry out the reconstruction. We also use the same formalism to investigate high resolution expansions fro...

In this paper, we generalize the concept of super edge-magic graph by introducing the new concept of super edge-magic models.

A graph G is called super edge-magic if there exists a bijective function f : V (G) ∪ E (G) → {1, 2, . . . , |V (G)|+ |E (G)|} such that f (V (G)) = {1, 2, . . . , |V (G)|} and f (u) + f (v) + f (uv) is a constant for each uv ∈ E (G). A graph G with isolated vertices is called pseudo super edge-magic if there exists a bijective function f : V (G) → {1, 2, . . . , |V (G)|} such that the set {f (...

Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic graph then q ≤ 2p− 3. Furthermore, if G is super edge-magic and q = 2p− 3, then the girth of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then q ≤ 2p − 5. In this paper we show that there are infinitely many graphs which are super edge-magic, have girth 5, and q =...

In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal (45◦) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A k-planar graph is a planar graph in which each vertex has degree less or equal to k. In particular, we prove that every 4-planar graph admits a planar...

A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G − X must have at least two vertices. The restricted connectivity κ′(G) of a connected graph G is defined as the minimum cardinality of a restricted cut. Additionally, if the deletion of a minimum restricted cut isolates on...

A subset F of edges in a connected graph G is a h-extra edge-cut if G − F is disconnected and every component has more than h vertices. The h-extra edge-connectivity λ(G) of G is defined as the minimum cardinality over all h-extra edge-cuts of G. A graph G, if λ(G) exists, is super-λ if every minimum h-extra edge-cut of G isolates at least one connected subgraph of order h + 1. The persistence ...