Bounds For Spectral Radius and Energy of $PIS$ Graphs

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

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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