an h-magic labeling in a h-decomposable graph g is a bijection f : v (g) ∪ e(g) → {1, 2, ..., p + q} such that for every copy h in the decomposition, σνεv(h) f(v) +  σeεe(h) f(e) is constant. f is said to be h-e-super magic if f(e(g)) = {1, 2, · · · , q}. a family of subgraphs h1,h2, · · · ,hh of g is a mixed cycle-decomposition of g if every subgraph hi is isomorphic to some cycle ck, for k ≥ ...

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...

Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).

The junction tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present a novel stochastic algorithm which we call the Christmas tree algorithm for building of junction trees sequentially by adding one node at a time to the underlying decomposable graph. The algorithm has two important theoretical properties. Firstly, every junc...

Given a decomposable graph, we characterize and enumerate the set of pairs of vertices whose connection or disconnection results in a new graph that is also decomposable. We discuss the relevance of this results to Markov chain Monte Carlo methods that sample or optimize over the space of decomposable graphical models according to probabilities determined by a posterior distribution given obser...

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...

A graph G is called randomly H − decomposable if every maximal H − packing in G uses all edges in G. G is called H − equipackable if every maximal H − packing in G is also a maximum H − packing in G. M2 − decomposable graphs, randomly M2 − decomposable graphs and M2 − equipackable graphs have been characterized. The definitions could be generalized to multigraphs. And M2 − decomposable multigra...

An additive hereditary graph property is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1, . . . ,Pn are graph properties, then a (P1, . . . ,Pn)-decomposition of a graph G is a partition E1, . . . , En of E(G) such that G[Ei], the subgraph of G induced by Ei, is in Pi, for i = 1, . . . , n. The sum of the properties P1, . . . ,Pn is the property P1 ⊕ · ·...