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

Muhammad Javaid
Additional contact information
Muhammad Javaid: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

Mathematics, 2017, vol. 5, issue 1, 1-12

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.

Keywords: adjacency matrix; least eigenvalue; bicyclic graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/5/1/18/pdf (application/pdf)
https://www.mdpi.com/2227-7390/5/1/18/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:5:y:2017:i:1:p:18-:d:92783

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().