A graph G= (V,E) with p vertices and q edges is called a Harmonic mean graph if it is possible to label the vertices xV with distinct labels f(x) from 1,2,....,q+1 in such a way that when each edge e=uv is labeled with f(uv)= ( ) ( ) ( ) ( ) (or) ( ) ( ) ( ) ( ) , then the edge labels are distinct. In this case, f is called Harmonic mean labeling of G. In this paper we prove that Double Triang...

In this paper we introduce a new type of labeling known as even vertex odd mean labeling. A graph G with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f : V (G) → {0, 2, 4, . . . , 2q−2, 2q} such that the induced map f∗ : E(G) → {1, 3, 5, . . . , 2q− 1} defined by f∗(uv) = f(u)+f(v) 2 is a bijection. A graph that admits an even ver...

In this paper, we introduce a new labeling called one modulo three mean labeling. A graph G is said to be one modulo three mean graph if there is an injective function φ from the vertex set of G to the set {a | 0 ≤ a ≤ 3q2 and either a≡0(mod 3) or a≡1(mod 3) } where q is the number of edges of G and φ induces a bijection φ * from the edge set of G to { } |1 3 2 and ( 3) a a q a 1 mod ≤ ≤ − ≡ gi...

BACKGROUND To examine empirically whether the mean difference (MD) or the standardised mean difference (SMD) is more generalizable and statistically powerful in meta-analyses of continuous outcomes when the same unit is used. METHODS From all the Cochrane Database (March 2013), we identified systematic reviews that combined 3 or more randomised controlled trials (RCT) using the same continuou...

A digraph D = (V,E) is a mod difference digraph if there exist a positive integer m and a labeling L : V → {1, 2, . . . , m − 1} such that (x, y) ∈ E if and only if L(y) − L(x) ≡ L(w)(mod m) for some w ∈ V. In this paper we prove that complete symmetric digraphs, unipaths and unicycles are mod difference digraphs.

We introduce indecomposable (hooked) Skolem sequences and we show their existence for all admissible orders. We then introduce a new construction for two-fold triple systems from two-fold Skolem sequences, and use this to motivate the concept of a two-fold Rosa sequence, whose existence we show for all admissible orders.

Expansion trees are defined as generalizations of Herbrand instances for formulas in a nonextensional form of higher-order logic based on Church’s simple theory of types. Such expansion trees can be defined with or without the use of skolem functions. These trees store substitution terms and either critical variables or skolem terms used to instantiate quantifiers in the original formula and th...