Smith, Bethany Joy2010-01-262010-01-2620062010-01-26http://hdl.handle.net/1828/2117Singly-periodic (SP) and doubly-periodic (DP) graphs arc infinite graphs which have translational symmetries in one and two dimensions, respectively. The problem of counting the number of connected components in such graphs is investigated. A method for determining whether or not an SP graph is k-colourable for a given positive integer k is given, and the question of deciding k-colourability of DP graphs is discussed. Colourings of SP and DP graphs can themselves be either periodic or aperiodic, and properties which determine the symmetries of their colourings arc also explored.enAvailable to the World Wide Webgraph theorygraph coloringUVic Subject Index::Sciences and Engineering::MathematicsThesis