From Osher Doctorow
In my M.A. Thesis at the University of London in social/cultural
anthropology in 1961 (I also have an M.A. in mathematics from USC 1969
and a Ph.D. in mathematical education from UCLA 1982), I studied
communication networks of wheel and cyclical and other types mentioned
in 199.1. My paper based on that Thesis was published in American
Anthropologist, April 1963, although there wasn't room to include most
of the details on the various networks. I also specialized in graph
theory combinatorics and other things including probability and
statistics in my M.A. coursework at USC and my Ph.D. coursework at
UCLA (together with differential equations).
Wolfram's "Chromatic number" depicts quite a few graphs including K6,
C5, C6, W5, W6 in the notation of 199.1. Cn for n = 2, 3, 4, ... is
just a regular polygon graph with vertices being the vertices of the
polygon and edges the edges of the polygon and no "diagonal" depicted
connecting vertices. Wn adds to Cn a line segment from the center of
the graph to each vertex, but no others. Star graphs Sn don't proceed
from Cn but Wn, deleting Cn (that is to say, deleting the boundary
edges of the polygon). So Sn is just a center point ("vertex")
connected by separate line segments to peripheral vertices, like the
spokes of a wheel without the boundary of the wheel.
Osher Doctorow
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