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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Main Authors: Indulal Gopalapilla, John Joy Mulloor, Liju Alex, Deena Scaria
Format: Article
Language:English
Published: University of Mohaghegh Ardabili 2025-06-01
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.
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institution Kabale University
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publishDate 2025-06-01
publisher University of Mohaghegh Ardabili
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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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AT deenascaria somegraphparametersofindubalaproductofgraphs