Numerical Range of Simple Graphs and Some Bounds for their Eigenvalues

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Tajarrod Maliheh; Sistani Tahereh

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Paper Information

Journal: JOURNAL OF MATHEMATICAL EXTENSION Year:2018 | Volume:12 | Issue:4 Page(s): 21-37

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Title

Numerical Range of Simple Graphs and Some Bounds for their Eigenvalues

Author(s)

Tajarrod Maliheh | Sistani Tahereh | Issue Writer Certificate

Keywords

Graph theory

adjacency matrix

eigenvalue of graphs

numerical range

Abstract

The numerical range of a simple graph G, named F(G), is the numerical range of its adjacency matrix A(G). The main purpose of this paper is to approximate F(G). Then, using this approximation, bounds for the largest and the smallest eigenvalues of G are proposed. In fact, lower bounds for the largest eigenvalues of G are presented in terms of disjoint induced subgraphs of G and the numerical range of the square of A(G).

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APA: Copy

Tajarrod, Maliheh, & Sistani, Tahereh. (2018). Numerical Range of Simple Graphs and Some Bounds for their Eigenvalues. JOURNAL OF MATHEMATICAL EXTENSION, 12(4), 21-37. SID. https://sid.ir/paper/719821/en

Vancouver: Copy

Tajarrod Maliheh, Sistani Tahereh. Numerical Range of Simple Graphs and Some Bounds for their Eigenvalues. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2018;12(4):21-37. Available from: https://sid.ir/paper/719821/en

IEEE: Copy

Maliheh Tajarrod, and Tahereh Sistani, “Numerical Range of Simple Graphs and Some Bounds for their Eigenvalues,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 12, no. 4, pp. 21–37, 2018, [Online]. Available: https://sid.ir/paper/719821/en

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