On the laplacian estrada index of a graph | Zendy

Jianxi Li | Zendy; Chee Shiu | Zendy; An Chang | Zendy

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On the laplacian estrada index of a graph

Author(s) -

Jianxi Li,

Chee Shiu,

An Chang

Publication year - 2009

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm0901147l

Subject(s) - mathematics , adjacency matrix , combinatorics , laplacian matrix , graph energy , eigenvalues and eigenvectors , graph , resistance distance , degree matrix , algebraic connectivity , laplace operator , spectral graph theory , discrete mathematics , graph power , line graph , mathematical analysis , physics , quantum mechanics

Let $G$ be a graph of order $n$. Let $lambda_{1}, lambda_{2},ldots, lambda_{n}$ be the eigenvalues of the adjacency matrix of$G$, and let $mu_{1}, mu_{2}, ldots, mu_{n}$ be the eigenvaluesof the Laplacian matrix of $G$. Much studied Estrada index of thegraph $G$ is defined as $EE=EE(G)=sumlimits^{n}_{i=1}e^{lambda_{i}}$. We define and investigate the Laplacian Estrada index of the graph $G$, $LEE=LEE(G)=sumlimits^{n}_{i=1}e^{(mu_{i}-frac{2m}{n})}$. Bounds for $LEE$ are obtained, as well as some relations between $LEE$ and graph Laplacian energy

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