On Partitional Labelings of Graphs

Abstract

The notion of partitional graphs, a subclass of sequential graphs, is introduced, and the cartesian product of a partitional graph and K 2 is shown to be partitional. Every sequential graph is harmonious and felicitous. The partitional property of some bipartite graphs including the n-dimensional cube Q n is studied, and thus this paper extends what was known about the sequentialness, harmoniousness and felicitousness of such graphs.

(Di)graph products, labelings and related results

“…Then und(D ⊗ h S k n ) is (super) edge-magic. Analogous results can be found in [20] when instead of assuming D (super) edge-magic we assume that D is one of the following types of labelings: (super) edge bi-magic [3,4], harmonious [14], sequential [13], partitional [16], cordial [6]. Almost all correspond to generalizations of previous results found in [15,19].…”

On Partitional and Other Related Graphs

“…All the partitional graphs included in this paper and in [11] satisfy the hypotheses of Theorems 4.1 and 4.3. Thus, these classes of graphs have strong α-valuations and strongly felicitous labelings.…”

“…The notion of partitional labelings was recently introduced by the authors in [11] as a tool for finding sequential, harmonious and felicitous labelings of various classes of bipartite graphs which are defined in terms of cartesian products. Let G be a bipartite graph with partite sets X and Y such that |X | = |Y | = s and |E(G)| = 2t +s for some positive integer t. Then a sequential labeling f of G is called a partitional labeling if f satisfies the following conditions:…”