Open Access. Powered by Scholars. Published by Universities.®
Discrete Mathematics and Combinatorics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 5 of 5
Full-Text Articles in Discrete Mathematics and Combinatorics
The Last Of The Mixed Triple Systems., Ernest Jum
The Last Of The Mixed Triple Systems., Ernest Jum
Electronic Theses and Dissertations
In this thesis, we consider the decomposition of the complete mixed graph on v vertices denoted Mv, into every possible mixed graph on three vertices which has (like Mv) twice as many arcs as edges. Direct constructions are given in most cases. Decompositions of theλ-fold complete mixed graph λMv, are also studied.
Independent Domination In Complementary Prisms., Joel Agustin Gongora
Independent Domination In Complementary Prisms., Joel Agustin Gongora
Electronic Theses and Dissertations
Let G be a graph and G̅ be the complement of G. The complementary prism GG̅ of G is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. For example, if G is a 5-cycle, then GG̅ is the Petersen graph. In this paper we investigate independent domination in complementary prisms.
Decompositions Of Mixed Graphs With Partial Orientations Of The P4., Adam M. Meadows
Decompositions Of Mixed Graphs With Partial Orientations Of The P4., Adam M. Meadows
Electronic Theses and Dissertations
A decomposition D of a graph H by a graph G is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. A mixed graph on V vertices is an ordered pair (V,C), where V is a set of vertices, |V| = v, and C is a set of ordered and unordered pairs, denoted (x, y) and [x, y] respectively, of elements of V [8]. An ordered pair (x …
Locating-Domination In Complementary Prisms., Kristin Renee Stone Holmes
Locating-Domination In Complementary Prisms., Kristin Renee Stone Holmes
Electronic Theses and Dissertations
Let G = (V (G), E(G)) be a graph and G̅ be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. A set D ⊆ V (G) is a locating-dominating set of G if for every u ∈ V (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N( …
Cyclic, F-Cyclic, And Bicyclic Decompositions Of The Complete Graph Into The 4-Cycle With A Pendant Edge., Daniel Shelton Cantrell
Cyclic, F-Cyclic, And Bicyclic Decompositions Of The Complete Graph Into The 4-Cycle With A Pendant Edge., Daniel Shelton Cantrell
Electronic Theses and Dissertations
In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:
(1) a single cycle of length v,
(2) f fixed points and a cycle of length v − f, or
(3) two disjoint cycles.
The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of Kv.