Physical Sciences and Mathematics Commons^™

Intersections And Representations Of Graphs, John Light

All Dissertations

Given two graphs G and H sharing the same vertex set, the edge-intersection spectrum of G and H is the set of possible
sizes of the intersection of the edge sets of both graphs. For example,
the spectrum of two copies of the cycle C₅ is {0, 2, 3, 5}, and the spectrum of two copies of the star K_1,r is {1, r}. The intersection spectrum was initially studied for designs by Lindner and Fu and others and was originally extended to graphs by Eric Mendelsohn. Several examples are studied, both when G and H are isomorphic and …