Properties of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic helm graph

Rizky P. Okfradifa, Siti Aminah, Kiki A. Sugeng

Research output: Contribution to journalConference articlepeer-review

Abstract

A directed unicyclic graph is a directed graph that has only one directed cycle subgraph. A directed unicyclic helm graph H-n is obtained from a directed wheel graph W-n by adjoining a directed pendant edge at each vertex of the cycle. A directed graph can be represented into several matrix representations, one of them is the antiadjacency matrix. The antiadjacency matrix is a matrix in which the entries represent whether there is a directed edge from one vertex to another. This paper discusses the general form of the coefficients of the characteristic polynomial that obtained by adding all of the determinants of antiadjacency matrix from each induced acyclic and cyclic subgraphs. The eigenvalues of the antiadjacency matrix of the directed unicyclic helm graph obtained by polynomial factorization. The result obtained denotes that the coefficients of the characteristic polynomial and eigenvalues of the antiadjacency matrix depend on the number of vertices of the cycle subgraphs of directed unicyclic helm graph.

Original languageEnglish
Article number012056
JournalJournal of Physics: Conference Series
Volume1722
Issue number1
DOIs
Publication statusPublished - 7 Jan 2021
Event10th International Conference and Workshop on High Dimensional Data Analysis, ICW-HDDA 2020 - Sanur-Bali, Indonesia
Duration: 12 Oct 202015 Oct 2020

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