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Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic

Author

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  • Muhammad Javaid

    (School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China)

Abstract

In a certain class of graphs, a graph is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. Let G 1 , n c and G 2 , n c be the classes of the connected graphs of order n whose complements are bicyclic with exactly two and three cycles, respectively. In this paper, we characterize the unique minimizing graph among all the graphs which belong to G n c = G 1 , n c ∪ G 2 , n c , a class of the connected graphs of order n whose complements are bicyclic.

Suggested Citation

  • Muhammad Javaid, 2017. "Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic," Mathematics, MDPI, vol. 5(1), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:1:p:18-:d:92783
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