On the existence of balanced bipartite designs, II

Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling 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 t...

Latin Square Type Bipartite Row-column Designs

A class of Balanced Bipartite Row-Column Designs (BBPRC-designs) in two sets of treatments of sizes v1=v and v2=v+1 with replications 2(v-1) and 2v, respectively, has been constructed by replacing the ii-th positions of 2v × 2v standard cyclic latin square design in 2v treatments by 2v treatments by (2v+1)-th treatment. Such design finds applications in agricultural and industrial experimentati...

Balanced nested designs and balanced arrays

Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric bal...

Some Balanced Bipartite Row-column Designs

A series of balanced bipartite row-column designs (BBPRC-designs) into sets of treatments with v1=4t+3 (test treatments) v2=2t+2 (control treatments) with varying replication has been obtained by supplementing a set of v2=2t+2 treatments in blank positions of non-orthogonal RC design of Agrawal (1966). Such designs find applications in agricultural and industrial experimentation where the inves...

Balanced bipartite 4-cycle designs