This paper introduces the notion of discrete t-set graceful graphs and obtains some of their properties. It also examines the interrelations among different types of set-indexers, namely, set-graceful, set-semigraceful, topologically set-graceful (t-set graceful), strongly t-set graceful and discrete t-set graceful and establishes how all these notions are interdependent or not. AMS Mathematics...

There are many results on edge-magic, and vertex-magic, labellings of finite graphs. Here we consider magic labellings of countably infinite graphs over abelian groups. We also give an example of a finite connected graph that is edge-magic over one, but not over all, abelian groups of the appropriate order.

Simple families of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size n all its increasing labellings, i.e., labellings of the nodes by distinct integers of the set {1, . . . , n} in such a way that each sequence of labels along any branch starting at the root is increasing. Three such tree families are of particular interest: recurs...

We investigate monomial labellings on cell complexes, giving a minimal cellular resolution of the ideal generated by these monomials, and such that the associated quotient ring is Cohen-Macaulay. We introduce a notion of such a labelling being maximal. There is only a finite number of maximal labellings for each cell complex, and we classify these for trees, partly for subdivisions of polygons,...

For a connected graph G of order n ≥ 3, let f : E(G) → Zn be an edge labeling of G. The vertex labeling f ′ : V (G) → Zn induced by f is defined as f (u) = ∑ v∈N(u) f(uv), where the sum is computed in Zn. If f ′ is one-to-one, then f is called a modular edge-graceful labeling and G is a modular edge-graceful graph. A modular edge-graceful labeling f of G is nowhere-zero if f(e) 6= 0 for all e ∈...