Laplacian Spectrum of Identity Graph of Commutative Ring Z 2 p $${\mathbb{Z}}_{2{\varvec{p}}}$$

DOI

10.2991/978-94-6463-148-7_17How to use a DOI?

Keywords

graph; spectrum; identity graph; commutative ring

Abstract

Research on the spectrum of a graph with an algebraic structure still attracts much attention. Let Z be a commutative ring. The I ( Z ) is a graph with set Z as its vertices and two vertices x , y ∈ Z are adjacent if and only if x . y = 1 , and also every vertex adjacent with 1. In 2020, research about Laplacian eigenvalues of a graph has been studied, that focuses on a zero divisor graph of ring Z n . This paper aims to determine the Laplacian spectrum of the identity graph of commutative ring Z 2 p , which can be constructed with investigate the eigenvalues of I ( Z 2 p ) . We find the set of all eigenvalues of I Z 2 p are integers.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Fidyatus Safitri
AU  - Purwanto
AU  - Santi Irawati
AU  - Wahyu Henky Irawan
PY  - 2023
DA  - 2023/05/29
TI  - Laplacian Spectrum of Identity Graph of Commutative Ring 
              
                Z
                
                  2
                  
                    p
                  
                
              
            $${\mathbb{Z}}_{2{\varvec{p}}}$$
BT  - Proceedings of the 12th International Conference on Green Technology (ICGT 2022)
PB  - Atlantis Press
SP  - 159
EP  - 165
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-148-7_17
DO  - 10.2991/978-94-6463-148-7_17
ID  - Safitri2023
ER  -