Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

Given two r-graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. The minimum number of parts in an H-decomposition of G is denoted by φH(G). By a 2-edge-decomposition of an r-graph we mean an H-decomposition for any fixed r-graph H with exactly 2 edges. In the special case where the two edges of...

A novel approach of edge detection is proposed that utilizes a bidimensional empirical mode decomposition (BEMD) method as the primary tool. For this purpose, a recently developed fast and adaptive BEMD (FABEMD) is used to decompose the given image into several bidimensional intrinsic mode functions (BIMFs). In FABEMD, order statistics filters (OSFs) are employed to get the upper and lower enve...

• Decompose the global thermodynamic entropy of a network into components associated with its edges. Calculate edge from partition functions classical and quantum statistics. Apply on synthetic real-world networks to evaluate qualitative quantitative differences in performance. In previous study, we have explored how decompose using graph-spectral decomposition technique. Here, develop this wor...

This paper analyzes the edge-reflection problem of obliquely incident guided waves in a plate. The generalized guided-wave theories in a plate, including the orthogonality of modes and the mode-decomposition method are summarized. The edge-reflection problem is solved on the basis of the mode-decomposition method. Some numerical results are presented and compared to experimental results. [doi:1...

Coupling methods for continuum models with molecular models are developed. Two methods are studied here: an overlapping domain decomposition method, which has overlapping domain, and an edge-to-edge decomposition method, which has an interface between two models. These two methods enforce the compatibility on the overlapping domain or interface nodes/atoms by the Lagrange multiplier method or t...

An H-decomposition of a graph G is a set L of edge-disjoint Hsubgraphs of G, such that each edge of G appears in some element of L. A k-orthogonal H-decomposition of a graph G is a set of k H-decompositions of G, such that any two copies of H in any two distinct H-decompositions have at most one edge in common. We prove that for every fixed graph H and every fixed integer k ≥ 1, if n is suffici...