Matrix Science Mathematic (MSMK)

EXTREMAL IOTA ENERGY OF A SUBCLASS OF TRICYCLIC DIGRAPHS AND SIDIGRAPHS

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msmk.02.2018.40.49

ABSTRACT

EXTREMAL IOTA ENERGY OF A SUBCLASS OF TRICYCLIC DIGRAPHS AND SIDIGRAPHS

Journal: Matrix Science Mathematic (MSMK)
Author: Fareeha Jamal, Mehtab Khan/span>

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2018.40.49

The iota energy of an n-vertex digraph D is defined by Ec (𝐷) = ∑ 􀀀1 |Im(𝑧 k)|, where z1, . . ., zn are eigenvalues of D and Im(zk) is the imaginary part of eigenvalue zk . The iota energy of an n-vertex sidigraph can be defined analogously. In this paper, we define a class Fn of n-vertex tricyclic digraphs containing five linear subdigraphs such that one of the directed cycles does not share any vertex with the other two directed cycles and the remaining two directed cycles are of same length sharing at least one vertex. We find the digraphs in Fn with minimal and maximal iota energy. We also consider a similar class of tricyclic sidigraphs and find extremal values of iota energy among the sidigraphs in this class.
Pages 40-49
Year 2018
Issue2 2
Volume 2

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