Expanders are classes of highly connected graphs that are of fundamental importance in graph theory, with numerous applications, especially in theoretical computer science [29]. While the literature contains various definitions of expanders, this paper focuses on bipartite expanders. For ∈ (0, 1], a bipartite graph G with bipartition V (G) = A ∪ B is a bipartite -expander if |A| = |B| and |N(S)...

In this paper, we study oriented bipartite graphs. particular, introduce “bitransitive” Several characterizations of bitransitive bitournaments are obtained. We show that bitounaments equivalent to acyclic bitournaments. As applications, characterize with Hamiltonian paths, determine the number non-isomorphic a given order, and solve graph-isomorphism problem in linear time for Next, prove well...

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.

An edge coloring of a graph G is a process of assigning colors to the adjacent edges so that the adjacent edges represents the different colors. In this paper, an algorithm is proposed to find the perfect color matching of the regular bipartite multigraph with low time complexity. For that, the proposed algorithm is divided into two procedures. In the first procedure, the possible circuits and ...

This paper considers the communication patterns arising from the partition of geometrical domain into sub-domains, when data is exchanged between processors assigned to adjacent sub-domains. It presents the algorithm constructing bipartite graphs covering the graph representation of the partitioned domain, as well as the scheduling algorithm utilizing the coloring of the bipartite graphs. Speci...