Bounds For Spectral Radius and Energy of $PIS$ Graphs

Year 2024, Volume: 9 Issue: 1, 26 - 35, 29.06.2024

Esra Öztürk Sözen , Elif Eryaşar

https://doi.org/10.33484/sinopfbd.1343041

https://izlik.org/JA63EX82FB

Abstract

Once the spectral radius and energy of a graph structure have been defined, many properties have been studied. The spectral radius and energy of a graph are related to the eigenvalues of the adjacency matrix of the graph. In this paper, we define an adjacency matrix for a prime ideal sum ($PIS$) graph and then extend the concepts of spectral radius and energy to $PIS$ graphs. Some bound theorems on the energy and spectral radius of $PIS$ graph structures are given. A SageMath code for plotting these graphs is also
provided.

Keywords

Graph energy , prime ideal sum graph , spectral radius

$PIS$ Grafların Spektral Yarıçapı ve Enerjisi İçin Sınırlar

https://izlik.org/JA63EX82FB

Abstract

Bir graf yapısının spektral yarıçapı ve enerjisi tanımlandıktan sonra birçok özelliği incelenmiştir. Grafların spektral yarıçapı ve enerjisi komşuluk matrisin özdeğerleriyle ilişkilidir. Bu çalışmada bir asal ideal toplam
($PIS$) graf için bir komşuluk matrisi tanımlanmıştır ve daha sonra spektral yarıçap ve enerji kavramları $PIS$ grafları için genişletilmiştir. $PIS$ graf yapılarının enerjisi ve spektral yarıçapına ilişkin bazı sınır teoremleri verilmiştir. Ayrıca bu grafları çizmek için bir SageMath kodu da sunulmaktadır.

Keywords

Graf enerjisi , asal ideal toplam graf , spektral yarıçap

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