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...

Abstract: This paper proposes a novel representation of decomposable graphs based on semi-latent tree-dependent bipartite graphs. The novel representation has two main benefits. First, it enables a form of subclustering within maximal cliques of the graph, adding informational richness to the general use of decomposable graphs that could be harnessed in applications with behavioural type of dat...

Let S(X) be a decomposable SPF with size |S| on commutative semiring (R,⊕,⊗, 0, 1), let d = |Xi| for all Xi ∈ X where X = (X1, . . . , Xn), and let the cost of a ⊕ b and a ⊗ b for any elements a, b ∈ R be c. Further, let e denote the complexity of evaluating any unary leaf function φj(Xi) in S and let k = maxv∈Ssum,j∈Ch(v) |Xv\Xj | < n, where Ssum, Sprod, and Sleaf are the sum, product, and lea...

If X ⊂ Pn is a projective non degenerate variety, the X-rank of a point P ∈ Pn is defined to be the minimum integer r such that P belongs to the span of r points of X. We describe the complete stratification of the fourth secant variety of any Veronese variety X via the X-rank. This result has an equivalent translation in terms both of symmetric tensors and homogeneous polynomials. It allows to...

We show that recursive circulant G(cd m ; d) is hamiltonian decomposable. Recursive circulant is a graph proposed for an interconnection structure of multicomputer networks in [8]. The result is not only a partial answer to the problem posed by Alspach that every connected Cayley graph over an abelian group is hamiltonian decomposable, but also an extension of Micheneau's that recursive circula...

In this paper, we study the problem of decomposing a given tensor into train such that tensors at vertices are orthogonally decomposable. When has length two, and decomposable two symmetric, recover decomposition by considering random linear combinations slices. Furthermore, if symmetric low-rank but not decomposable, show whitening procedure can transform orthogonal case. network three or more...

We introduce the notion of an Eulerian graph being strongly evencycle decomposable, and note that a few basic classes have this property. Our main results are that several fundamental composition operations that preserve the property of being Eulerian also preserve the property of being strongly even-cycle decomposable. As an application, our composition operations easily imply that all Euleria...