DOI: https://doi.org/10.14710/jfma.v6i1.16653

ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS

*Aluysius Sutjijana orcid scopus publons  -  Departement Matematika FMIPA UGM, Indonesia
Dea Alvionita Azka  -  Institut Teknologi Muhammadiyah Sumatera, Musi Rawas, Indonesia, Indonesia

Citation Format:
Abstract

Let G be an undirected graphs with no multiple edges. There are many ways to represent a graph, and one of them is in a matrix form, by constructing an antiadjacency matrix. Given a connected graph G with  vertex set $V$ consisting of n members, an antiadjacency matrix of the graph G is a matrix B of order n \times n such that if there is an edge that connects vertex v_i to vertex v_j (v_i \sim v_j ) then the element of i^{th} row and b^{th} column of B is 0, otherwise 1. In this paper we investigate some properties of antiadjacency matrices for some strong product of two graphs. Our results are general forms of the antiadjacency matrix of the strong product of path graphs P_m with P_n for m, n\ge 3, and cycle graphs C_m with C_m for m \ge 3.

Fulltext View|Download
Keywords: Keywords: antiadjacency matrix, strong product, path graph, cycle graph .
Funding: Departemen Matematika FMIPA UGM under contract MU127/J01.1.28/PL.06.02/2019.

Article Metrics:

Article Info
Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
Recent articles
ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION A CLOSER LOOK AT A PATH DOMINATION NUMBER IN GRID GRAPHS More recent articles
  1. D. Azka, ,D. Junia Eksi Palupi, and A. Sutjijana, (2022). Dimensi Metrik Lokal dari Hasil Perkalian Kuat Graf Bintang, Jurnal Fourier, 11(2), 49–58
  2. Carlson, S.C. 2017, Graph Theory, Encyclopaedia Britannica, 1–10. (Online) : https://www.britannica.com/topic/graph-theory
  3. Balakrishnan,R. dan Ranganathan,K., 2012, A Textbook of Graph Theory,Springer, New York
  4. G. Chartrand,G. and P. Zhang, A First Course in Graph Theory, Dover Publication,Inc., New York, 2012
  5. Chartrand,G., Lesniak,L. dan Zhang,P., 2016, Graphs and Digraphs (sixth edition), Taylor Francis Graph, New York
  6. M. Aouchiche, P. Hansen, Distance spectra of graphs: A survey, Linear Algebra Appl. 458 (2014) 301–386
  7. A.E. Brouwer, W.H. Haemers, Spectra of Graphs, Springer, New York, 2012
  8. D. Cvetkovi´c, M. Doob, H. Sachs, Spectra of Graphs: Theory and Applications, Academic Press, New York, San Francisco, London, 1980. 3 rev. and enl. ed. Heidelberg, Leipzig, Barth, 1995
  9. D. Cvetkovi´c, P. Rowlinson, S. Simi´c, Eigenspaces of Graphs, Cambridge University Press, Cambridge, 1997
  10. F. Harary, and R.A Melter, ”On the Metric Dimension of a Graph”, ars. Combine, 2,
  11. - 195, 1976
  12. M. Edwina, and K. A. Sugeng, ”Determinant of Antiadjacency Matrix of Union and Join Operation from Two Disjoint of Several Classes of Graphs”, AIP Publishing, 978-0-7354-1536-2, 030158-1, 2016
  13. N. Selvia, N. Paramita, K.A. Sugeng, and S. Utama, ”Sifat Nilai Eigen Matriks Antiadja-cency dari Graf Asiklik”, Seminar Nasional Matematika, UI-Unpad, 2015
  14. D. Diwyacitta, A. P. Putra, K. A. Sugeng, S. Utama, ”The Determinant of An Antiadja-cency Matrix of a Direct Cycle Graph with Chords”, AIP Publishing, 978-0-7354-1536-2, 030127-1, 2016
  15. R.B. Bapat, Graph and Martices, Spinnger: Berlin, 2010
  16. R. Hammack, W. Imrich, and S. Klavzar, Handbook of Product Graphs Second Edition, Taylor and Francis Group, USA, 2010
  17. Khuller,S., Raghavachari,B., dan Rosenfeld,A., 1996, Landmarks in Graphs, Discrete Appl.Math, 70: 3, 217-229

Last update:

No citation recorded.

Last update:

No citation recorded.