Characteristic polynomial and eigenvalues of antiadjacency matrix of directed cyclic dumbbell graph with cycles of different sizes

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Abstract

This paper explains the characteristic polynomial and eigenvalues of the antiadjacency matrix of a directed cyclic dumbbell graph. Antiadjacency matrix of a directed graph is a matrix whose entries represent whether there exist a directed edge connecting two vertices in the directed graph or not. The coefficients of the characteristic polynomial of the antiadjacency matrix of directed cyclic dumbbell graph is obtained by evaluating the determinant of each induced subgraph of the directed cyclic dumbbell graph and by counting the number of certain forms of induced subgraph of the directed cyclic dumbbell graph. The eigenvalues of the antiadjacency matrix of directed cyclic dumbbell graph is obtained by polynomial factorization. The result obtained show that the coefficients of the characteristic polynomial and the eigenvalues of antiadjacency matrix of directed cyclic dumbbell graph can be expressed as a function that is dependent to the number of vertices of the cycle subgraphs of directed cyclic dumbbell graph.

Original languageEnglish
Title of host publication4th IndoMS International Conference on Mathematics and its Applications, IICMA 2019
EditorsDadam Kusnandar, Yundari Yundari, Evi Noviani
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735420311
DOIs
Publication statusPublished - 15 Sep 2020
Event4th IndoMS International Conference on Mathematics and its Applications, IICMA 2019 - Pontianak, Indonesia
Duration: 23 Sep 201925 Sep 2019

Publication series

NameAIP Conference Proceedings
Volume2268
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference4th IndoMS International Conference on Mathematics and its Applications, IICMA 2019
CountryIndonesia
CityPontianak
Period23/09/1925/09/19

Keywords

  • Antiadjacency matrix
  • Characteristic polynomial
  • Directed cyclic graph
  • Dumbbell graph
  • Eigenvalues
  • Induced subgraph

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