Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic
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...
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| Format: | Article |
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MDPI AG
2017-03-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/5/1/18 |
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| author | Muhammad Javaid |
| author_facet | Muhammad Javaid |
| author_sort | Muhammad Javaid |
| collection | DOAJ |
| description | 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. |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-13T06:00:28Z |
| publishDate | 2017-03-01 |
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| spelling | doaj.art-d8356d30df594210ae80b6dd6b312c672022-12-21T23:57:21ZengMDPI AGMathematics2227-73902017-03-01511810.3390/math5010018math5010018Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are BicyclicMuhammad Javaid0School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, ChinaIn 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.http://www.mdpi.com/2227-7390/5/1/18adjacency matrixleast eigenvaluebicyclic graphs |
| spellingShingle | Muhammad Javaid Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic Mathematics adjacency matrix least eigenvalue bicyclic graphs |
| title | Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic |
| title_full | Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic |
| title_fullStr | Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic |
| title_full_unstemmed | Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic |
| title_short | Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic |
| title_sort | characterization of the minimizing graph of the connected graphs whose complements are bicyclic |
| topic | adjacency matrix least eigenvalue bicyclic graphs |
| url | http://www.mdpi.com/2227-7390/5/1/18 |
| work_keys_str_mv | AT muhammadjavaid characterizationoftheminimizinggraphoftheconnectedgraphswhosecomplementsarebicyclic |