In this article, we introduce the concept of a near a-labeling of a bipartite graph, and prove that if a graph G with n edges has a near a-labeling, then there ...

It is proved that if a graph G with n edges has a near a-labeling, then there is a cyclic G-decomposition of both Kn,n and K2nx+1 for all positive integers ...

An α-labelings of a bipartite graph G with n edges easily yields both a cyclic G-decomposition of Kn,n and of K2nx+1 for all positive integers x.

A labeling (or valuation) of a graph G is an assignment of integers to the vertices of G subject to certain conditions. A hierarchy of graph labelings was ...

We give several new families of graphs that have α-labelings. We also present some evidence to support the conjecture that every bipartite graph G ...

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the ...

Aug 3, 2015 · α is the cardinality of the biggest independent set (no pair of vertices is connected) and β is the cardinality of the smallest covering by ...

In this note we show that the α-labeling number of a bipartite graph G is bounded, which proves a conjecture of Snevily. Previous article in issue

A graceful labeling of a bipartite graph is an α-labeling if it has the property that the labels assigned to the vertices of one stable set of the graph are ...

Abstract. The weak tensor product was introduced by Snevily as a way to construct new graphs that admit α-labelings from a pair of known α-graphs.