Author
Ramesh Prasad Panda
Other affiliations: Indian Institute of Technology Guwahati, Homi Bhabha National Institute, Indian Institute of Technology Kanpur
Bio: Ramesh Prasad Panda is an academic researcher from National Institute of Science Education and Research. The author has contributed to research in topics: Vertex (geometry) & Cyclic group. The author has an hindex of 5, co-authored 16 publications receiving 70 citations. Previous affiliations of Ramesh Prasad Panda include Indian Institute of Technology Guwahati & Homi Bhabha National Institute.
Papers
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TL;DR: The power graph of a group G is the graph whose vertex set is G and two distinct vertices are adjacent if one is a power of the other as mentioned in this paper, and the minimal separating sets of power g...
Abstract: The power graph of a group G is the graph whose vertex set is G and two distinct vertices are adjacent if one is a power of the other. This paper investigates the minimal separating sets of power g...
29 citations
TL;DR: In this article, the minimum degree, indescrete power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup.
Abstract: The enhanced power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we consider the minimum degree, ind...
22 citations
TL;DR: In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups is obtained, and it is ascertained that the edge-connectivity of the power graphs is bounded.
Abstract: In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity ...
13 citations
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TL;DR: It is proved that the notion of equality of the vertex connectivity and the algebraic connectivity andThe notion of Laplacian integral are equivalent for power graphs of dicyclic groups.
Abstract: In this article, various aspects of Laplacian spectra of power graphs of finite cyclic, dicyclic and finite $p$-groups are studied. Algebraic connectivity of power graphs of the above groups are considered and determined completely for that of finite $p$-groups. Further, the multiplicity of Laplacian spectral radius of power graphs of the above groups are studied and determined completely for that of dicyclic and finite $p$-groups. The equality of the vertex connectivity and the algebraic connectivity is characterized for power graphs of all of the above groups. Orders of dicyclic groups, for which their power graphs are Laplacian integral, are determined. Moreover, it is proved that the notion of equality of the vertex connectivity and the algebraic connectivity and the notion of Laplacian integral are equivalent for power graphs of dicyclic groups. All possible values of Laplacian eigenvalues are obtained for power graphs of finite $p$-groups. This shows that power graphs of finite $p$-groups are Laplacian integral.
12 citations
TL;DR: In this article, various aspects of Laplacian spectra of power graphs of finite cyclic, dicyclic and finite p-groups are considered and the algebraic connectivity is studied.
Abstract: In this article, various aspects of Laplacian spectra of power graphs of finite cyclic, dicyclic and finite p-groups are considered. The algebraic connectivity is studied and the multiplicity of the Laplacian spectral radius is determined completely for power graphs of all of these groups. Then the equality of the vertex connectivity and the algebraic connectivity is characterized for power graphs of all of the above groups. Orders of dicyclic groups, for which their power graphs are Laplacian integral, are determined. Moreover, it is proved that the notion of equality of the vertex connectivity and the algebraic connectivity and the notion of Laplacian integral are equivalent for power graphs of dicyclic groups. All possible values of Laplacian eigenvalues are obtained for power graphs of finite p-groups. This shows that power graphs of finite p-groups are Laplacian integral.
11 citations
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01 Jan 2009
TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.
Abstract: Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.
398 citations
01 Jan 2016
TL;DR: An introduction to the theory of graph spectra is available in the book collection an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.
Abstract: an introduction to the theory of graph spectra is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the an introduction to the theory of graph spectra is universally compatible with any devices to read.
222 citations
TL;DR: This paper aims to demonstrate the efforts towards in-situ applicability of EMMR-II, which aims to provide real-time information about the response of the immune system to EMTs.
37 citations
TL;DR: In this paper, the enhanced power graph is defined as the graph with vertex set G such that two vertices x and y are adjacent if they are contained in the same cyclic subgroup.
Abstract: The enhanced power graph 𝒢e(G) of a group G is the graph with vertex set G such that two vertices x and y are adjacent if they are contained in the same cyclic subgroup. We prove that finite groups...
26 citations
TL;DR: In this article, the minimum degree, indescrete power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup.
Abstract: The enhanced power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we consider the minimum degree, ind...
22 citations