F-Continuous Graphs |
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| Authors: | Gary Chartrand Elzbieta B Jarrett Farrokh Saba Ebrahim Salehi Ping Zhang |
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| Institution: | (1) Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA;(2) Engineering, Mathematics and Physical Sciences Division, Modesto Junior College, Modesto, CA 95350, USA;(3) Department of Mathematics and Computer Science, University of Detroit Mercy, Detroid, MI 48219, USA;(4) Department of Mathematics Sciences, University of Nevada, Las Vegas, NV 89154, USA |
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| Abstract: | For a nontrivial connected graph F, the F-degree of a vertex  in a graph G is the number of copies of F in G containing . A graph G is F-continuous (or F-degree continuous) if the F-degrees of every two adjacent vertices of G differ by at most 1. All P3-continuous graphs are determined. It is observed that if G is a nontrivial connected graph that is F-continuous for all nontrivial connected graphs F, then either G is regular or G is a path. In the case of a 2-connected graph F, however, there always exists a regular graph that is not F-continuous. It is also shown that for every graph H and every 2-connected graph F, there exists an F-continuous graph G containing H as an induced subgraph. |
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| Keywords: | F-degree F-degree continuous |
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