A new method of model registration is proposed using graphical templates. A graph of landmarks is chosen in the template image. All possible candidates for these landmarks are found in the data image using local operators. A dynamic programming algorithm on decomposable subgraphs of the template graph nds the optimal match to a subset of the candidate points in polynomial time. This combination...

A signed graph (G,Σ) is a G together with set Σ⊆E(G) of negative edges. circuit positive if the product signs its edges positive. balanced all circuits are The frustration index l(G,Σ) minimum cardinality E⊆E(G) such that (G−E,Σ−E) balanced, and k-critical l(G,Σ)=k l(G−e,Σ−e)<k, for every e∈E(G). We study decomposition subdivision critical graphs completely determine t-critical graphs, t≤2. Cri...

Let S = {K1,3,K3, P4} be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph G into graphs taken from any non-empty S′ ⊆ S. The problem is known to be NP-complete for any possible choice of S′ in general graphs. In this paper, we assume that the input graph is cubic, and study the computational complexity of the problem of partitioning its edge se...

An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1, . . . , m} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K2 has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomp...

A new method of model registration is proposed using graphical templates. A graph of landmarks is chosen in the template image. All possible candidates for these landmarks are found in the data image using local operators. A dynamic programming algorithm on decomposable subgraphs of the template graph finds the optimal match to a subset of the candidate points in polynomial time. This combinati...

According to Gestalt theory, any image is perceived subconsciously as a coherent structure (or whole) with two contrast substructures: figure and ground. The consists of numerous autogenerated substructures an inherent hierarchy far more smalls than larges. Through these substructures, the structural beauty (L), or equivalently livingness space, can be computed by multiplication number (S) thei...

Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

‎Recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎In this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎Then we use this construction to generalize the result due to Cook and Nagel‎.

Let g be a fixed element of a finite group G. We introduce the g-noncommuting graph of G whose vertex set is whole elements of the group G and two vertices x,y are adjacent whenever [x,y] g  and  [y,x] g. We denote this graph by . In this paper, we present some graph theoretical properties of g-noncommuting graph. Specially, we investigate about its planarity and regularity, its clique number a...

Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen-Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) the Castelnuovo-Mumford regularity of R/I(G) can be determined from the invariants of G.