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Full-Text Articles in Physical Sciences and Mathematics
Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux
Restrained And Other Domination Parameters In Complementary Prisms., Wyatt Jules Desormeaux
Electronic Theses and Dissertations
In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or …
Double Domination Of Complementary Prisms., Lamont D. Vaughan
Double Domination Of Complementary Prisms., Lamont D. Vaughan
Electronic Theses and Dissertations
The complementary prism of a graph G is obtained from a copy of G and its complement G̅ by adding a perfect matching between the corresponding vertices of G and G̅. For any graph G, a set D ⊆ V (G) is a double dominating set (DDS) if that set dominates every vertex of G twice. The double domination number, denoted γ×2(G), is the cardinality of a minimum double dominating set of G. We have proven results on graphs of small order, specific families and lower bounds on γ×2 …
Finding Edge And Vertex Induced Cycles Within Circulants., Trina Marcella Wooten
Finding Edge And Vertex Induced Cycles Within Circulants., Trina Marcella Wooten
Electronic Theses and Dissertations
Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As …
On The Attainability Of Upper Bounds For The Circular Chromatic Number Of K4-Minor-Free Graphs., Tracy Lance Holt
On The Attainability Of Upper Bounds For The Circular Chromatic Number Of K4-Minor-Free Graphs., Tracy Lance Holt
Electronic Theses and Dissertations
Let G be a graph. For k ≥ d ≥ 1, a k/d -coloring of G is a coloring c of vertices of G with colors 0, 1, 2, . . ., k - 1, such that d ≤ | c(x) - c(y) | ≤ k - d, whenever xy is an edge of G. We say that the circular chromatic number of G, denoted χc(G), is equal to the smallest k/d where a k/d -coloring exists. In [6], Pan and …