Some graph parameters of Indu-Bala product of graphs
The Indu-Bala product of graphs G and H consists of two disjoint copies of the join of G and H such that there is an adjacency between the corresponding vertices in the two copies of H. A vertex subset S of a graph G = (V, E) is said to be a geodetic set if every vertex in G is in some u−v geodesic...
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University of Mohaghegh Ardabili
2025-06-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_3792_36735edc013bb5d4d0b43ff01ef9022a.pdf |
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| author | Indulal Gopalapilla John Joy Mulloor Liju Alex Deena Scaria |
| author_facet | Indulal Gopalapilla John Joy Mulloor Liju Alex Deena Scaria |
| author_sort | Indulal Gopalapilla |
| collection | DOAJ |
| description | The Indu-Bala product of graphs G and H consists of two disjoint copies of the join of G and H such that there is an adjacency between the corresponding vertices in the two copies of H. A vertex subset S of a graph G = (V, E) is said to be a geodetic set if every vertex in G is in some u−v geodesic, where u and v are any two vertices in S. The minimum cardinality of such a set is the geodetic number of G. The vertex subset D of a graph G is said to be a dominating set if every vertex in G is either in D or adjacent to at least one vertex in D. The minimum cardinality of such a set is the domination number of G. In this work, the authors studied various geodetic and dominating extensions with respect to the Indu-Bala product of graphs. The Aα matrix associated with a graph is a convex linear combination of its adjacency matrix and degree diagonal matrix, offering deeper insights into the properties of both matrices. In this article the authors discuss the Aα spectrum of Indu-Bala product of graphs. |
| format | Article |
| id | doaj-art-cfb0c24e67f64c03887b5303ae271e10 |
| institution | Kabale University |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-cfb0c24e67f64c03887b5303ae271e102025-08-20T03:50:05ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662025-06-01141576710.22098/jhs.2025.16039.10543792Some graph parameters of Indu-Bala product of graphsIndulal Gopalapilla0John Joy Mulloor1Liju Alex2Deena Scaria3Department of Mathematics, St Aloysius College, Edathua-689573,Kerala, India,1Department of Mathematics, St. Stephens College, Uzhavoor - 686634, Kerala, IndiaDepartment of Mathematics, Bishop Chulaparambil Memorial(BCM) College, Kottayam - 686001, Kerala, IndiaDepartment of Mathematics, Marthoma College, Thiruvalla, 689 103, Kerala, India,The Indu-Bala product of graphs G and H consists of two disjoint copies of the join of G and H such that there is an adjacency between the corresponding vertices in the two copies of H. A vertex subset S of a graph G = (V, E) is said to be a geodetic set if every vertex in G is in some u−v geodesic, where u and v are any two vertices in S. The minimum cardinality of such a set is the geodetic number of G. The vertex subset D of a graph G is said to be a dominating set if every vertex in G is either in D or adjacent to at least one vertex in D. The minimum cardinality of such a set is the domination number of G. In this work, the authors studied various geodetic and dominating extensions with respect to the Indu-Bala product of graphs. The Aα matrix associated with a graph is a convex linear combination of its adjacency matrix and degree diagonal matrix, offering deeper insights into the properties of both matrices. In this article the authors discuss the Aα spectrum of Indu-Bala product of graphs.https://jhs.uma.ac.ir/article_3792_36735edc013bb5d4d0b43ff01ef9022a.pdfextreme vertexuniversal vertexgeodetic numberdomination numberindu-bala productaα spectrum |
| spellingShingle | Indulal Gopalapilla John Joy Mulloor Liju Alex Deena Scaria Some graph parameters of Indu-Bala product of graphs Journal of Hyperstructures extreme vertex universal vertex geodetic number domination number indu-bala product aα spectrum |
| title | Some graph parameters of Indu-Bala product of graphs |
| title_full | Some graph parameters of Indu-Bala product of graphs |
| title_fullStr | Some graph parameters of Indu-Bala product of graphs |
| title_full_unstemmed | Some graph parameters of Indu-Bala product of graphs |
| title_short | Some graph parameters of Indu-Bala product of graphs |
| title_sort | some graph parameters of indu bala product of graphs |
| topic | extreme vertex universal vertex geodetic number domination number indu-bala product aα spectrum |
| url | https://jhs.uma.ac.ir/article_3792_36735edc013bb5d4d0b43ff01ef9022a.pdf |
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