On Vertex-Edge Degree Based Properties of Sierpinski Graphs

Abstract

Network science and graph theory are two important branches of mathematics and computer science. Many problems in engineering and physics are modeled with networks and graphs. Topological analysis of networks enable researchers to analyse networks in relation some physical and engineering properties without conducting expensive experimental studies. Topological indices are numerical descriptors which defined by using degree, distance and eigen-value notions in any graph. Most of the topological indices are defined as by using classical degree concept in graph theory, network and computer science. Recently two novel degree parameters have been defined in graph theory: Vertex-edge degree and Edge-vertex degree. Vertex-edge degree and edge-vertex degree based topological indices have been defined as parallel to their corresponding classical degree counterparts. Generalized Sierpinski networks have an important place of applications in view of engineering science especially in computer science. Classical degree based topological properties of generalized Sierpinski graphs have been investigated by many studies. In this article, vertex-edge degree based topological indices values of generalized Sierpinski graphs have been computed.

Keywords

• Vertex-edge degree
• Vertex-edge degree based topological indices
• Topological indices
• Generalized Sierpinski graphs

Sierpinski Graflarının Tepe-Ayrıt Temelli Derece Özellikleri Üzerine

Öz

Ağ bilimi ve graf teorisi, matematik ve bilgisayar biliminin iki önemli dalıdır. Mühendislik ve fizikle ilgili birçok problem, ağlar ve graflarla modellenir. Ağların topolojik analizi, araştırmacıların pahalı deneysel çalışmalar yürütmeden, ağları bazı fiziksel ve mühendislik özellikleriyle ilgili olarak analiz etmelerini sağlar. Topolojik indeksler, herhangi bir grafta derece, uzaklık ve öz değer kavramları kullanılarak tanımlanan sayısal tanımlayıcılardır. Topolojik indekslerin çoğu, graf teorisi, ağ ve bilgisayar bilimlerinde klasik derece kavramı kullanılarak tanımlanır. Yakın zamanda graf teorisinde iki yeni derece parametresi tanımlanmıştır: Tepe-ayrıt derecesi ve ayrıt-tepe derecesi. Tepe-ayrıt ve ayrıt-tepe derece temelli topolojik indeksler, klasik derece karşılıklarına parallel olarak tanımlanmıştır. Genelleştirilmiş Sierpinski ağları mühendislik bilimi açısından özellikle bilgisayar bilimleri açısından önemli bir uygulama alanına sahiptir. Genelleştirilmiş Sierpinski graflarının klasik derece tabanlı topolojik özellikleri birçok çalışmada incelenmiştir. Bu makalede, genelleştirilmiş Sierpinski grafiklerinin tepe-ayrıt derece temelli topolojik indeks değerleri hesaplandı.

Anahtar Kelimeler

• Tepe-ayrıt derecesi
• Tepe-ayrıt derece temelli topolojik indeksler
• Topolojik indeksler
• Genelleştirilmiş Sierpinski grafları

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