THE MAIN EIGENVALUES OF THE UNDIRECTED POWER GRAPH OF A GROUP

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JAVARSINEH MEHRNOOSH; FATH TABAR GHOLAM HOSSEIN

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Journal Paper

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Journal: Algebraic structures and their applications Year:2017 | Volume:4 | Issue:1 Page(s): 19-32

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Title

THE MAIN EIGENVALUES OF THE UNDIRECTED POWER GRAPH OF A GROUP

Author(s)

JAVARSINEH MEHRNOOSH | FATH TABAR GHOLAM HOSSEIN | Issue Writer Certificate

Keywords

Power graph

Main eigenvalue

Cyclic group

Prime divisor

Abstract

The undirected Power graph of a nite group G, P(G), is a graph with the group elements of G as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let A be an adjacency matrix of P(G). An eigenvalue of A is a Main eigenvalue if the eigenspace "( ) has an eigenvector X such that Xtj 6= 0, where j is the all-one vector. In this paper we want to focus on the Power graph of the nite Cyclic group Zn and nd a condition on n where P(Zn) has exactly one Main eigenvalue. Then we calculate the number of Main eigenvalues of P(Zn) where n has a unique prime decomposition n = prp2. We also formulate a conjecture on the number of the Main eigenvalues of P(Zn) for an arbitrary positive integer n.

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APA: Copy

JAVARSINEH, MEHRNOOSH, & FATH TABAR, GHOLAM HOSSEIN. (2017). THE MAIN EIGENVALUES OF THE UNDIRECTED POWER GRAPH OF A GROUP. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, 4(1), 19-32. SID. https://sid.ir/paper/354233/en

Vancouver: Copy

JAVARSINEH MEHRNOOSH, FATH TABAR GHOLAM HOSSEIN. THE MAIN EIGENVALUES OF THE UNDIRECTED POWER GRAPH OF A GROUP. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS[Internet]. 2017;4(1):19-32. Available from: https://sid.ir/paper/354233/en

IEEE: Copy

MEHRNOOSH JAVARSINEH, and GHOLAM HOSSEIN FATH TABAR, “THE MAIN EIGENVALUES OF THE UNDIRECTED POWER GRAPH OF A GROUP,” ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, vol. 4, no. 1, pp. 19–32, 2017, [Online]. Available: https://sid.ir/paper/354233/en

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