The least eigenvalue of the graphs whose complements are connected and have pendent paths

• Autorzy: Wang C. , Yu G. , Sun W. , Cao J.

Identyfikatory

DOI

10.1515/jaiscr-2018-0020

• Języki publikacji: EN

Abstrakty

EN

The adjacency matrix of a graph is a matrix which represents adjacent relation between the vertices of the graph. Its minimum eigenvalue is defined as the least eigenvalue of the graph. Let Gn be the set of the graphs of order n, whose complements are connected and have pendent paths. This paper investigates the least eigenvalue of the graphs and characterizes the unique graph which has the minimum least eigenvalue in Gn.

Słowa kluczowe

EN

graph; complement; pendent path; adjacency matrix; least eigenvalue

• Wydawca: University of Social Sciences
• Czasopismo: Journal of Artificial Intelligence and Soft Computing Research
• Rocznik: 2018
• Tom: Vol. 8, No. 4
• Strony: 303--308
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Wang C.

• School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China

autor

Yu G.

• School of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246133, China

autor

Sun W.

• School of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246133, China

autor

Cao J.

• School of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China

Bibliografia

• [1] F. Bell, D. Cvetkovic, P. Rowlinson, S. Simić, Graph for which the least eigenvalues is minimal,I. Linear Algebra Appl., 429, 2008, 234-241.
• [2] F. Bell, D. Cvetkovic, P. Rowlinson, S. Simić,Graph for which the least eigenvalues is minimal,II. Linear Algebra Appl., 429, 2008, 2168-2176.
• [3] D. Cardoso, D. Cvetkovic, P. Rowlinson, S. Simić,A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph, Linear Algebra Appl., 429, 2008, 2770-2780.
• [4] Y. Fan, Y. Wang, Y. Gao, Minimizing the least eigenvalues of unicyclic graphs with application to spectralspread, Linear Algebra Appl., 429, 2008, 577-588.
• [5] Y. Fan, F. Zhang, Y. Wang, The least eigenvalue of the complements of tree, Linear Algebra Appl., 435, 2011, 2150-2155.
• [6] W. Haemers, Interlacing eigenvalues and graphs, Linear Algebra Appl., 227-228, 1995, 593-616.
• [7] S. Li, S. Wang, The least eigenvalue of the signless Laplacian of the complements of trees, Linear Algebra Appl., 436, 2012, 2398-2405.
• [8] R. Liu, M. Zhai, J. Shu Th,e least eigenvalues of unicyclic graph with n vertices and k pendant vertices. Linear Algebra Appl., 431, 2009, 657-665.
• [9] M. Petrovic, B. Borovićanin, T. Aleksić, Bicyclic graphs for which the least eigenvalue is minimum.Linear Algebra Appl., 430, 2009, 1328-1335.
• [10] Y. Tan, Y. Fan, The vertex(edge) independence number, vertex(edge) cover number and the least eigenvalue of a graph, Linear Algebra Appl., 433, 2010, 790-795.
• [11] Y. Wang, Y. Fan, The least eigenvalue of a graph with cut vertices. Linear Algebra Appl., 433, 2010, 19-27.
• [12] Y. Wang, Y. Fan, X. Li, et al. The least eigenvalue of graphs whose complements are unicyclic,Discussiones Mathematicae Graph Theory, 35(2), 2013, 1375-1379.
• [13] M. Ye, Y. Fan, D. Liang. The least eigenvalue of graphs with given connectivity. Linear Algebra Appl., 430, 2009, 1375-1379.
• [14] G. Yu, Y. Fan, Y. Wang, Quadratic forms on graphs with application to minimizing the least eigenvalue of signless Laplacian over bicyclic graphs, Electronic J. Linear Algebra, 27, 2014, 213-236.
• [15] G. Yu, Y. Fan. The least eigenvalue of graphs. Math. Res. Expo., 32(6), 2012, 659-665.
• [16] G.Yu, Y.Fan, The least eigenvalue of graphs whose complements are 2-vertex or 2-edge connected, Operations Research Transactions, 17(2), 2013, 81-88.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).