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Mathematics 2017, 5(1), 18; doi:10.3390/math5010018

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

School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
Academic Editor: Lokenath Debnath
Received: 29 December 2016 / Revised: 27 February 2017 / Accepted: 27 February 2017 / Published: 11 March 2017
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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. View Full-Text
Keywords: adjacency matrix; least eigenvalue; bicyclic graphs adjacency matrix; least eigenvalue; bicyclic graphs
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Javaid, M. Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic. Mathematics 2017, 5, 18.

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