Additively weighted harary index pada graf pembagi nol dari ring bilangan bulat modulo p³

ABSTRAK Skripsi ini meneliti Indeks Additively Weighted Harary pada Graf Pembagi Nol dari Ring Bilangan Bulat Modulo p^3, di mana p adalah bilangan prima. Penelitian ini menggunakan analisis matematika yang mencakup identifikasi himpunan pembagi nol tak-nol, perhitungan derajat titik dalam graf, dan perhitungan jarak antar titik. Proses ini penting dalam mengembangkan formula umum yang akurat untuk Indeks additively weighted Harary. Hasil signifikan dari penelitian ini adalah formula indeks additively weighted Harary khususnya pada graf pembagi nol dari ring bilangan bulat modulo p^3. Hasil penelitian ini tidak hanya menjabarkan teori graf dan aritmetika modular, tetapi juga memberikan pendekatan baru dalam menganalisis sifat-sifat struktur dari graf pembagi nol dari ring bilangan bulat modulo p^3 ABSTRACT This research explores the Additively Weighted Harary Index on Zero-Divisor Graphs of the Ring of Integers Modulo p^3, where p is a prime number. The study employs an advanced mathematical analysis including identifying the non-zero zero-divisor set, calculating vertex degrees within the graph, and measuring inter-vertex distances. This process is instrumental in developing an accurate general formula for the Additively Weighted Harary Index. The significant outcome of this research is the derivation of the formula for this index specifically for zero-divisor graphs in the integer ring modulo p^3. This work not only augments the understanding of graph theory and modular arithmetic but also provides a novel approach to analyzing properties of these mathematical structures مستخلص البحث هذا البحث تستكشف مؤشر additively weighted Harary على مخطط القسام الصفرية لحلقة الأعداد الصحيحة موديولو p^3، حيث p عدد أولي. يتضمن الدراسة تحليلًا رياضيًا متقدمًا تشمل تحديد مجموعة القسام الصفرية غير الصفرية، وحساب درجة الرؤوس داخل المخطط، وقياس المسافات بين الرؤوس. هذه العملية الأساسية في تطوير الصيغة العامة الدقيقة لمؤشر additively weighted Harary. النتيجة البارزة لهذا البحث هي استنتاج الصيغة لهذا المؤشر خصيصًا لمخطط القسام الصفرية في حلقة الأعداد الصحيحة موديولو p^3. هذا العمل لا يعزز فقط فهم نظرية المخطط والحساب الموديولي ولكن يوفر أيضًا منهجًا جديدًا لتحليل خصائص هذه الخصائص الهياك

Survey on topological indices and graphs associated with a commutative ring

The researches on topological indices are initially related to graphs obtained from biological activities or chemical structures and reactivity. Recently, the research on this topic has evolved on graphs in general and even on graphs obtained from algebraic structures, such as groups, rings or modules. This paper will present various topological index concepts, various graph concepts obtained from a commutative ring and some previous studies that are relevant to those two concepts. Based on the various concepts presented, research topics related to topological indices of a graph associated with a commutative ring can be found and carried out

Some Topological Indices of Subgroup Graph of Symmetric Group

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Product version of reciprocal degree distance of composite graphs

In this paper‎, ‎we present the upper bounds for the product version of reciprocal degree distance of the tensor product‎, ‎join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices‎