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 ≥ ...

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 ≥ ...

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, ∑νεV (H) f(v) + ∑νεE (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 ≥...

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...

A (d,h)-decomposition of a graph G is an order pair (D,H) such that H subgraph where has the maximum degree at most h and D acyclic orientation G−E(H) out-degree d. (d,h)-decomposable if (d,h)-decomposition. Let be embeddable in surface nonnegative characteristic. It known (d,h)-decomposable, then h-defective d+1-choosable. In this paper, we investigate graphs prove following four results. (1) ...

A graph G is ramdomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H , can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize all ramdomly P3– decomposable graphs and ramdomly P4–decomposable graphs. We also characterize all ramdomly Pk–decomposable graphs of size 2k where all vertices have even ...

We call a vertex x of a graph G = (V,E) a codominated vertex if NG[y] ⊆ NG[x] for some vertex y ∈ V \{x}, and a graph G is called codismantlable if either it is an edgeless graph or it contains a codominated vertex x such that G − x is codismantlable. We show that (C4, C5)-free vertex-decomposable graphs are codismantlable, and prove that if G is a (C4, C5, C7)-free well-covered graph, then ver...

Su, X.-Y., A result on decompositions of regular graphs, Discrete Mathematics 105 (1992) 323-326. We prove that for any connected graph G and any integer r which is a common multiple of the degrees of the vertices in G, there exists a connected, r-regular, and G-decomposable graph H such that x(H) = x(G) and o(H) = w(G), where x and w are the chromatic number and the clique number, respectively...

Given a graph G $G$ , decomposition of is partition its edges. A ( d h ) $(d,h)$ -decomposable if edge set can be partitioned into $d$ -degenerate and with maximum degree at most $h$ . For ≤ 4 $d\le 4$ we are interested in the minimum integer ${h}_{d}$ such that every planar $(d,{h}_{d})$ -decomposable. It was known 3 ${h}_{3}\le 2 8 ${h}_{2}\le 8$ 1 = ∞ ${h}_{1}=\infty $ This paper proves ${h}...

An H-magic labeling in an 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, ∑ v∈V (H) f(v)+ ∑ e∈E(H) f(e) is constant. The function f is said to be H-E-super magic if f(E(G)) = {1, 2, . . . , q}. In this paper, we study some basic properties of m-factor-E-super magic labeling and we provide a necessary and sufficient cond...