A balanced coloring of a graph G means a triple {P1, P2,X} of mutually disjoint subsets of the vertex-set V (G) such that V (G) = P1⊎P2⊎X and |P1| = |P2|. A balanced decomposition associated with the balanced coloring V (G) = P1⊎P2⊎X of G is defined as a partition of V (G) = V1⊎· · ·⊎Vr (for some r) such that, for every i ∈ {1, · · · , r}, the subgraphG[Vi] of G is connected and |Vi∩P1| = |Vi∩P...

If each subgraph of the decomposition π graph G has Steiner number same as then is said to be a G. The maximum cardinality among and denoted by πst(G). In this paper, we present for Complete n-Sun graph.

Nonlinear optimization problems are found at the heart of real-time operations critical infrastructures. These computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these as graph-structured problems, and illustrate how their structure can be exploited level (for parallelizing function/derivative computations) solver linear ...

HYPERGRAPH MODELS FOR SPARSE MATRIX PARTITIONING AND REORDERING  Umit V. C ataly urek Ph.D. in Computer Engineering and Information Science Supervisor: Assoc. Prof. Cevdet Aykanat November, 1999 Graphs have been widely used to represent sparse matrices for various scienti c applications including one-dimensional (1D) decomposition of sparse matrices for parallel sparse-matrix vector multiplic...

This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs hav...

Finding appropriate bound sets of variables is the most important task of functional decomposition. When solving some problems the bound sets need to be large; for instance in decomposition to symmetric subfunctions realized in MOPS arrays for submicron technologies, or when no good small bound sets exist. In such cases the creation of the incompatibility graph, that is necessary to evaluate go...