K1, pq-factorization of complete bipartite graphs

META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS

The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...

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...

Mixed cycle-E-super magic decomposition of complete bipartite graphs

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...

P7-factorization of complete bipartite graphs

Chordal bipartite graphs of bounded tree- and clique-width

A bipartite graph is chordal bipartite if every cycle of length at least six has a chord. In the class of chordal bipartite graphs the tree-width and the clique-width are unbounded. Our main results are that chordal bipartite graphs of bounded vertex degree have bounded tree-width and that k-fork-free chordal bipartite graphs have bounded clique-width, where a k-fork is the graph arising from a...