The distance spectrum of corona and cluster of two graphs
Let G be a connected graph with a distance matrix D. The D-eigenvalues {μ1,μ2,…,…,μp} of G are the eigenvalues of D and form the distance spectrum or D-spectrum of G. Given two graphs G with vertex set {v1,v2,……,vp} and H, the corona G∘H is defined as the graph obtained by taking p copies of H and f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2015-11-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860015000419 |
| _version_ | 1811289209024020480 |
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| author | G. Indulal Dragan Stevanović |
| author_facet | G. Indulal Dragan Stevanović |
| author_sort | G. Indulal |
| collection | DOAJ |
| description | Let G be a connected graph with a distance matrix D. The D-eigenvalues {μ1,μ2,…,…,μp} of G are the eigenvalues of D and form the distance spectrum or D-spectrum of G. Given two graphs G with vertex set {v1,v2,……,vp} and H, the corona G∘H is defined as the graph obtained by taking p copies of H and for each i, joining the ith vertex of G to all the vertices in the ith copy of H. Let H be a rooted graph rooted at u. Then the cluster G{H} is defined as the graph obtained by taking p copies of H and for each i, joining the ith vertex of G to the root in the ith copy of H. In this paper we describe the distance spectrum of G∘H, for a connected distance regular graph G and any r-regular graph H in terms of the distance spectrum of G and adjacency spectrum of H. We also describe the distance spectrum of G{Kn}, where G is a connected distance regular graph. |
| first_indexed | 2024-04-13T03:50:53Z |
| format | Article |
| id | doaj.art-1ed2561a32734444b1cfb5c765e6f654 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 |
| language | English |
| last_indexed | 2024-04-13T03:50:53Z |
| publishDate | 2015-11-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-1ed2561a32734444b1cfb5c765e6f6542022-12-22T03:03:50ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002015-11-0112218619210.1016/j.akcej.2015.11.014The distance spectrum of corona and cluster of two graphsG. Indulal0Dragan Stevanović1Department of Mathematics, St. Aloysius College, Edathua, Alappuzha 689573, IndiaUniversity of Primorska, Institute Andrej Marusic, Muzejski trg 2, 6000 Koper, SloveniaLet G be a connected graph with a distance matrix D. The D-eigenvalues {μ1,μ2,…,…,μp} of G are the eigenvalues of D and form the distance spectrum or D-spectrum of G. Given two graphs G with vertex set {v1,v2,……,vp} and H, the corona G∘H is defined as the graph obtained by taking p copies of H and for each i, joining the ith vertex of G to all the vertices in the ith copy of H. Let H be a rooted graph rooted at u. Then the cluster G{H} is defined as the graph obtained by taking p copies of H and for each i, joining the ith vertex of G to the root in the ith copy of H. In this paper we describe the distance spectrum of G∘H, for a connected distance regular graph G and any r-regular graph H in terms of the distance spectrum of G and adjacency spectrum of H. We also describe the distance spectrum of G{Kn}, where G is a connected distance regular graph.http://www.sciencedirect.com/science/article/pii/S0972860015000419Distance spectrumCoronaCluster |
| spellingShingle | G. Indulal Dragan Stevanović The distance spectrum of corona and cluster of two graphs AKCE International Journal of Graphs and Combinatorics Distance spectrum Corona Cluster |
| title | The distance spectrum of corona and cluster of two graphs |
| title_full | The distance spectrum of corona and cluster of two graphs |
| title_fullStr | The distance spectrum of corona and cluster of two graphs |
| title_full_unstemmed | The distance spectrum of corona and cluster of two graphs |
| title_short | The distance spectrum of corona and cluster of two graphs |
| title_sort | distance spectrum of corona and cluster of two graphs |
| topic | Distance spectrum Corona Cluster |
| url | http://www.sciencedirect.com/science/article/pii/S0972860015000419 |
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