The Eigen-3-Cover Ratio of Graphs: Asymptotes, Domination and Areas
Journal: Global Journal of Mathematics (GJM) (Vol.3, No. 1)Publication Date: 2015-05-15
Authors : Carol Lynne Jessop; Paul August Winter;
Page : 256-266
Keywords : Energy of graphs; eigenvalues; vertex 3-cover; domination; ratios; asymptotes; areas.;
- The Eigen-Cover Ratio of Graphs: Asymptotes, Domination and Areas
- The Eigen-3-Cover Ratio of Graphs: Asymptotes, Domination and Areas
- Finding minimal Ferrers-esque graphs on path graphs ans cycle graphs via set cover
- INDEPENDENT DOMINATION NUMBER OF EULER TOTIENT CAYLEY GRAPHS AND ARITHMETIC GRAPHS
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Abstract
The separate study of the two concepts of energy and vertex coverings of graphs has opened many avenues of research. In this paper we combine these two concepts in a ratio, called the eigen-3-cover ratio, to investigate the domination effect of the subgraph induced by a vertex 3-covering of a graph (called the 3-cover graph of ), on the original energy of , where large number of vertices are involved. This is referred to as the eigen-3-cover domination and has relevance, in terms of conservation of energy, when a molecule’s atoms and bonds are mapped onto a graph with vertices and edges, respectively. If this energy-3-cover ratio is a function of , the order of graphs belonging to a class of graph, then we discuss its horizontal asymptotic behavior and attach the graphs average degree to the Riemann integral of this ratio, thus associating eigen-3-cover area with classes of graphs. We found that the eigen-3-cover domination had a strongest effect on the complete graph, while this eigen-3-cover domination had zero effect on star graphs. We show that the eigen-3-cover asymptote of discussed classes of graphs belong to the interval [0,1], and conjecture that the class of complete graphs has the largest eigen-3-cover area of all classes of graphs.
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