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Showing 1 to 8 of 8 for “"Petersen Graph"”.
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Excluding Two Minors of the Petersen Graph
… we begin with a brief survey of the Petersen graph and its role in graph theory. We will then develop an alternative decomposition to clique sums for 3-connected graphs, called T-sums. This decomposition will be used in Chapter 2 to completely characterize those graphs which have no …
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Independent Domination in Complementary Prisms.
<p>Let <em>G</em> be a graph and <em>G̅</em> be the complement of <em>G</em>. The complementary prism <em>GG̅</em> of <em>G</em> is the graph formed from the disjoint union of <em>G</em> and <em>G̅</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em> and …
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Edge-colorings and flows in Class 2 graphs
We consider edge-colorings and flows problems in Graph Theory that are hard to solve for Class 2 graphs. Most of them are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the …
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Measurements of edge uncolourability in cubic graphs
The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such …
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Bipartite Density of Generalized Petersen Graphs
The bipartite density b(G) of a graph G with m edges is the maximum ratio [special characters omitted] where m0 is the number of edges in a bipartitesubgraph of G. In this study we determine the bipartite density of several classes of Generalized Petersen Graphs. These graphs are denoted by P(n, …
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Topological Approaches to Chromatic Number and Box Complex Analysis of Partition Graphs
Determining the chromatic number of the partition graph P(33) poses a considerable challenge. We can bound it to 4 ≤ χ(P(33)) ≤ 6, with exhaustive search confirming χ(P(33)) = 6. A potential mathematical proof strategy for this equality involves identifying a Z2-invariant S4 with non-trivial …
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Dynamics on networks
… consider two dynamical models whose underlying graph can be represented by a single network. We first consider the Kuramoto model, a canonical model of coupled phase oscillators. We obtain two results on its partial phase-locked state, where a subset of oscillators remain close in phase while …
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Groups, Graphs, and Symmetry-Breaking
A labeling of a graph G is said to be r-distinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an r-distinguishing labeling on G is called the distinguishing number of G. The distinguishing set of a group Gamma, D(Gamma), is the set …