Graphical analyses of connected-kernel scattering equations

Simple graphical techniques are employed to obtain a new (simultaneous) derivation of a large class of connected-kernel scattering equations. This class includes the Rosenberg, Bencze-Redish-Sloan, and connected-kernel multiple scattering equations as well as a host of generalizations of these and other equations. The basic result is the application of graphical methods to the derivation of interaction-set equations. This yields a new, simplified form for some members of the class and elucidates the general structural features of the entire class