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...

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the lab...

Let G be a graph and f : V (G) → {1, 2, 3, . . . , p+ q} be an injection. For each edge e = uv and an integer m ≥ 2, the induced Smarandachely edge m-labeling f∗ S is defined by f ∗ S(e) = ⌈ f(u) + f(v) m ⌉ . Then f is called a Smarandachely super m-mean labeling if f(V (G))∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, . . . , p+ q}. Particularly, in the case of m = 2, we know that f ∗(e) =    f(u)+f(v) ...

Encoding the clustering result to represent the structure feature of a tree ‹ Encoding each cluster as following field ‹Link all cluster fields to make a long numeric array that can represent the structure of a tree Describing the trees' super‐sub relationships with a network, and using a numeric method to access it fast. PURPOSE ‡ Structure Network: A network describing the super‐sub relations...

Until now, all super-resolution algorithms have presumed that the images were taken under the same illumination conditions. This paper introduces a new approach to super-resolution—based on edge models and a local blur estimate—which circumvents these difficulties. The paper presents the theory and the experimental results using the