NULLITY AND ENERGY OF THE CUBIC POWER GRAPH

NULLITY AND ENERGY OF THE CUBIC POWER GRAPH

O. Ejima, T. T. Chelvam, K. O. Aremu

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Abstract

Let G be a  nite abelian group with identity 0; G1 = f3t j t 2 Gg   G and G2 = G n G1: The cubic power graph Tcpg of G is an undirected simple graph with vertex set G, such that two distinct vertices x and y are adjacent in Tcpg if and only if x + y 2 G1 n f0g: In this paper, we  rst prove certain properties of the cubic power graph Tcpg of  nite abelian groups. Finally, we observe some properties on the nullity of the cubic power graph Tcpg and also show that the energy of the cubic power graph of a  nite abelian group of order n is bounded below by r (n - 3)(n - 1) 3 if n is divisible by 3 and n - 1 if n otherwise.

Keywords

Univalent functions, Analytic functions, Second Hankel determinant, Logarithmic coe cients, Close-to-convex function.