THE EIGENVALUES AND ENERGY OF INTEGRAL CIRCULANT GRAPHS

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MOLLAHAJIAGHAEI MOHSEN

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Journal: TRANSACTIONS ON COMBINATORICS Year:2012 | Volume:1 | Issue:3 Page(s): 47-56

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Information Journal Paper

Title

THE EIGENVALUES AND ENERGY OF INTEGRAL CIRCULANT GRAPHS

Author(s)

MOLLAHAJIAGHAEI MOHSEN | Issue Writer Certificate

Keywords

GRAPHQ2

INTEGRAL CIRCULANT GRAPHQ2

EIGENVALUEQ2

ENERGYQ2

Abstract

A GRAPH is called circulant if it is a Cayley GRAPH on a cyclic group, i.e. its adjacency matrix is circulant. Let D be a set of positive, proper divisors of the integer n > 1. The integral circulant GRAPH ICGn (D) has the vertex set Z n and the edge set E (ICGn (D)) = {{a, b}; gcd (a – b, n) Î D}. Let n = p1p2….pkm, where p1, p2, …., pk are distinct prime numbers and gcd (p1p2…pk, m) = 1. The open problem posed in paper [A. Ilic, The ENERGY of unitary Cayley GRAPHs, Linear Algebra Appl., 431 (2009) 1881-1889] about calculating the ENERGY of an arbitrary integral circulant ICGn (D) is completely solved in this paper, where D = {p1, p2, …., pk}.

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APA: Copy

MOLLAHAJIAGHAEI, MOHSEN. (2012). THE EIGENVALUES AND ENERGY OF INTEGRAL CIRCULANT GRAPHS. TRANSACTIONS ON COMBINATORICS, 1(3), 47-56. SID. https://sid.ir/paper/213778/en

Vancouver: Copy

MOLLAHAJIAGHAEI MOHSEN. THE EIGENVALUES AND ENERGY OF INTEGRAL CIRCULANT GRAPHS. TRANSACTIONS ON COMBINATORICS[Internet]. 2012;1(3):47-56. Available from: https://sid.ir/paper/213778/en

IEEE: Copy

MOHSEN MOLLAHAJIAGHAEI, “THE EIGENVALUES AND ENERGY OF INTEGRAL CIRCULANT GRAPHS,” TRANSACTIONS ON COMBINATORICS, vol. 1, no. 3, pp. 47–56, 2012, [Online]. Available: https://sid.ir/paper/213778/en

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