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Full-Text Articles in Physical Sciences and Mathematics
Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski
Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski
Dissertations and Theses
An orthomorphism, π, of a group, (G, +), is a permutation of G with the property that the map x → -x + π(x) is also a permutation. In this paper, we consider orthomorphisms of the additive group of binary n-tuples, Zn2. We use known orthomorphism preserving functions to prove a uniformity in the cycle types of orthomorphisms that extend certain partial orthomorphisms, and prove that extensions of particular sizes of partial orthomorphisms exist. Further, in studying the action of conjugating orthomorphisms by automorphisms, we find several symmetries within the orbits and stabilizers of this action, and …
Tree Graphs And Orthogonal Spanning Tree Decompositions, James Raymond Mahoney
Tree Graphs And Orthogonal Spanning Tree Decompositions, James Raymond Mahoney
Dissertations and Theses
Given a graph G, we construct T(G), called the tree graph of G. The vertices of T(G) are the spanning trees of G, with edges between vertices when their respective spanning trees differ only by a single edge. In this paper we detail many new results concerning tree graphs, involving topics such as clique decomposition, planarity, and automorphism groups. We also investigate and present a number of new results on orthogonal tree decompositions of complete graphs.