For any kEN, a graph G = (V, E) is said to be ;:z k-magic if there exists a labeling Z: E( G) --+ ;:z k {OJ such that the induced vertex set labeling Z+: V (G) --+ ;:z k defined by Z+(v) = L Z(uv) uvEE(G) is a constant map. For a given graph G, the set of all kEN for which G is ;:z k-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper we will consider the func...

Let G = (V,E) be a graph. If G is a König graph or if G is a graph without 3-cycles and 5-cycles, we prove that the following conditions are equivalent: ∆G is pure shellable, R/I∆ is Cohen-Macaulay, G is an unmixed vertex decomposable graph and G is well-covered with a perfect matching of König type e1, . . . , eg without 4-cycles with two ei’s. Furthermore, we study vertex decomposable and she...

For any h ∈ N, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh − {0} such that the induced vertex labeling l : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h ∈ N for which G admits a zero-sum h-magic labeling. A graph G is said to b...

We prove that the Petersen colouring conjecture implies a conjecture of Markström saying that the line graph of every bridgeless cubic graph is decomposable into cycles of even length. In addition, we describe two infinite families of 4regular graphs: the first family consists of 3-connected graphs with no even cycle decomposition and the second one consists of 4-connected signed graphs with no...

Given an abelian group A, a graph G = (V, E) is said to have a distance two magic labeling in A if there exists a labeling l : E(G) → A − {0} such that the induced vertex labeling l∗ : V (G) → A defined by l∗(v) = ∑ e∈E(v) l(e) is a constant map, where E(v) = {e ∈ E(G) : d(v, e) < 2}. The set of all h ∈ Z+ for which G has a distance two magic labeling in Zh is called the distance two magic spec...

For any h ∈ Z, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh−{0} such that the induced vertex set labeling l : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. For a given graph G, the set of all h ∈ Z+ for which G is h-magic is called the integermagic spectrum of G and is denoted by IM (G). In this paper, we will determine the integer-magic sp...

For any positive integer k, a graph G = (V, E) is said to be ZZ k-magic if there exists a labeling l : E(G) −→ ZZ k − {0} such that the induced vertex set labeling l : V (G) −→ ZZ k defined by l(v) = ∑ { l(uv) : uv ∈ E(G) } is a constant map. For a given graph G, the set of all h ∈ ZZ + for which G is ZZ h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, w...

A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2, . . . , |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to 1+|E(G)| 2 deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.

Let G = (V,E) be a graph of order n and size e. An (a, d)-vertexantimagic total labeling is a bijection α from V (G) ∪ E(G) onto the set of consecutive integers {1, 2, . . . , n + e}, such that the vertex-weights form an arithmetic progression with the initial term a and the common difference d. The vertex-weight of a vertex x is the sum of values α(xy) assigned to all edges xy incident to the ...