Spatial autocorrelation, of which Geary’s c has traditionally been a popular measure, is fundamental to spatial science. This paper provides new perspective on c. We discuss this using concepts from spectral graph theory/linear algebraic theory. More precisely, we provide three types representations for it: (a) Laplacian representation, (b) Fourier transform and (c) Pearson’s correlation coeffi...

For a given number of colors, $s$, the guessing graph is (base $s$) logarithm cardinality largest family colorings vertex set such that color each can be determined from colors vertices in its neighborhood. This quantity related to problems network coding, circuit complexity and entropy. We study graphs as property context classic extremal questions, relationship forbidden subgraph property. fi...

Two boards are rook equivalent if they have the same number of non-attacking placements for any rooks. Define a equivalence graph on an class Ferrers by specifying that two connected edge you can obtain one moving squares in other board out column and into single column. Given such graph, we characterize which will yield graphs. We also provide some cases where common graphs or not be set board...