On the Corona of Two Graphs.
On the Corona of Two Graphs. (Short Communication).
On the cost chromatic number of outerplanar, planar, and line graphs
We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost chromatic number of maximal outerplanar and maximal planar graphs can be arbitrarily large and construct...
On the counting of fully packed loop configurations: some new conjectures.
On the Covering Multiplicity of Lattices.
On the crossing number of .
On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six
The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. According to their special structure, the class of Cartesian products of two graphs is one of few graph classes for which some exact values of crossing numbers were obtained. The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. Moreover, except of six graphs, the crossing numbers of Cartesian products G⃞K1,n for all other...
On the crossing numbers of Cartesian products of stars and paths or cycles
On the Crossing Numbers of Cartesian Products of Wheels and Trees
Bokal developed an innovative method for finding the crossing numbers of Cartesian product of two arbitrarily large graphs. In this article, the crossing number of the join product of stars and cycles are given. Afterwards, using Bokal’s zip product operation, the crossing numbers of the Cartesian products of the wheel Wn and all trees T with maximum degree at most five are established.
On the crossing numbers of G □ Cₙ for graphs G on six vertices
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. The crossing numbers of G☐Cₙ for some graphs G on five and six vertices and the cycle Cₙ are also given. In this paper, we extend these results by determining crossing numbers of Cartesian products G☐Cₙ for some connected graphs G of order six with six and seven edges. In addition, we collect known results concerning crossing numbers of G☐Cₙ for graphs G on six vertices.
On the crossing numbers of graphs
On the crossing numbers of and
On the cutting edge: simplified planarity by edge addition.
On the -Splitting Graph of a Graph
On the decomposition of complete directed graphs into factors with given radii
On the Decomposition of the Complete Directed Graph into Factors with Given Diameters
On The Decomposition Of The Line (Total) Graphs With Respct To Some Binary Operations
On the Decompositions of Complete Graphs into Cycles and Stars on the Same Number of Edges
Let Cm and Sm denote a cycle and a star on m edges, respectively. We investigate the decomposition of the complete graphs, Kn, into cycles and stars on the same number of edges. We give an algorithm that determines values of n, for a given value of m, where Kn is {Cm, Sm}-decomposable. We show that the obvious necessary condition is sufficient for such decompositions to exist for different values of m.
On the defining number for vertex colorings of a family of graphs.
On the degree of regularity of generalized van der Waerden triples.