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Formation of graph models for regular finite element meshes

Kaveh A., Koohestani K.

Computer Assisted Mechanics and Engineering Sciences

2009

Vol. 16, No. 2

101-115

Graph theory has many applications in structural mechanics and there are also numerous topological transformations which make the related problems simpler. The skeleton graph and natural associate graph of finite element models are among such transformations. These transformations can efficiently be used for nodal and element ordering of regular finite element models. Natural associate graph and its mesh basis play a key role in optimal finite element analysis by combinatorial force method. In this paper, an efficient method is presented for generation of skeleton graph, natural associate graph as well as their mesh bases for finite elements models, using graph and digraph products.

Domatic number of graph products

Kijewska M.

Journal of Mathematics and Applications

2008

Vol. 30

71-81

A partition of V(G), all of whose classes arę dominating sets in G, is called a domatic partition of G. The maximum number of classes of a domatic partition of G is called the domatic nuraber of G. In this paper we explore the bounds for the domatic numbers of the cartesian product, the strong product and the join of two graphs. The bounds are the best possible in the sense that there exist examples for which equalities are attained.