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Bipartite Graph
Domination Number
Independence Number
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On the Estrada and Laplacian Estrada indices of graphs
On the Estrada and Laplacian Estrada indices of graphs,10.1016/j.laa.2011.03.057,Linear Algebra and Its Applications,Zhibin Du,Zhongzhu Liu
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On the Estrada and Laplacian Estrada indices of graphs
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Zhibin Du
,
Zhongzhu Liu
The Estrada index of a graph G is defined as EE(G)=∑i=1neλi, where λ1,λ2,…,λn are the eigenvalues of G. The Laplacian Estrada index of a graph G is defined as LEE(G)=∑i=1neμi, where μ1,μ2,…,μn are the Laplacian eigenvalues of G. An edge grafting operation on a graph moves a pendent edge between two pendent paths. We study the change of Estrada index of graph under edge grafting operation between two pendent paths at two adjacent vertices. As the application, we give the result on the change of Laplacian Estrada index of
bipartite graph
under edge grafting operation between two pendent paths at the same vertex. We also determine the unique tree with minimum Laplacian Estrada index among the set of trees with given maximum degree, and the unique trees with maximum Laplacian Estrada indices among the set of trees with given diameter, number of pendent vertices, matching number,
independence number
and domination number, respectively.
Journal:
Linear Algebra and Its Applications  LINEAR ALGEBRA APPL
, vol. 435, no. 8, pp. 20652076, 2011
DOI:
10.1016/j.laa.2011.03.057
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(1)
Distribution system adequacy assessment accounting customer controlled generator sets
L. D. Arya
,
L. S. Titare
,
D. P. Kothari
Journal:
International Journal of Electrical Power & Energy Systems  INT J ELEC POWER ENERG SYST
, vol. 33, no. 5, pp. 11611164, 2011