โ Scribed by Felix Lazebnik; Andrew J. Woldar
No coin nor oath required. For personal study only.
In this paper we present a simple method for constructing infinite families of graphs defined by a class of systems of equations over commutative rings. We show that the graphs in all such families possess some general properties including regularity and biregularity, existence of special vertex colorings, and existence of covering mapsโhence, embedded spectraโbetween every two members of the same family. Another general property, recently discovered, is that nearly every graph constructed in this manner edgeโdecomposes either the complete, or complete bipartite, graph which it spans. In many instances, specializations of these constructions have proved useful in various graph theory problems, but especially in many extremal problems. A short survey of the related results is included. We also show that the edgeโdecomposition property allows one to improve existing lower bounds for some multicolor Ramsey numbers. ยฉ 2001 John Wiley & Sons, Inc. J Graph Theory 38: 65โ86, 2001
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## A Computer Aided Modeling Program (CAMP) is developed to process a bond graph representation of a physical engineering system into suitable source input used by Digital Simulation Languages such as IBM DSL (Digital Simulation Language), CSMP (Continuous System Modeling Program), ACSL (Advanced Co