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الرئيسية > An Atlas of K-Distance Neighbo...>الوصف

An Atlas of K-Distance Neighborhood Polynomials of Graphs with at most Six Vertices

المصدر: مجلة جامعة البيضاء
الناشر: جامعة البيضاء
المؤلف الرئيسي: Naji, Ahmed M. (Author)
مؤلفين آخرين: Mahde, Sultan Senan (Co-Author)
المجلد/العدد: مج5, ع4
محكمة: نعم
الدولة: اليمن
التاريخ الميلادي: 2023
الشهر: نوفمبر
الصفحات: 569 - 583
ISSN: 2709-9695
رقم MD: 1456212
نوع المحتوى: بحوث ومقالات
اللغة: الإنجليزية
قواعد المعلومات: EduSearch, HumanIndex
مواضيع:
المعادلات الرياضية | الرسوم البيانية | كثيرات الحدود
كلمات المؤلف المفتاحية:
Second Degree (Of Vertex) | Distance | Graph Polynomial
رابط المحتوى:
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المستخلص: In a connected graph 𝐺 = ( , 𝐸 ) , the distance from a vertex 𝑣 to a vertex 𝑢 , denoted 𝑑 ( 𝑢 , 𝑣 ) , is the length of the shortest path joins them. For a vertex 𝑣 in 𝐺 , the eccentricity 𝑒 ( 𝑣 ) is the distance to the farthest vertex from 𝑣 and for 0 ≤ 𝑘 ≤ 𝑒 ( 𝑣 ) , the 𝑘 -distance degree (𝑘 -degree) of 𝑣 , is 𝑑 𝑘 ( 𝑣 ) = { 𝑢 ∈ 𝑉 ( 𝐺 ) : 𝑑 ( 𝑣 , 𝑢 ) = 𝑘 } . The 𝑁 𝑘 -polynomial of a graph 𝐺 is a distance degree-based topological polynomial and is denoted by 𝑁 𝑘 ( , 𝑥 ) . It is a polynomial with the coefficient of the term , and is equal to the sum of 𝑑 𝑘 ( 𝑣 ) , for every 𝑣 ∈ 𝑉 ( 𝐺 ) . The roots of an 𝑁 𝑘 -polynomial of a graph are called the 𝑁 𝑘 -roots of 𝐺 and denoted by 𝑍 ( 𝑘 ( 𝐺 , 𝑥 ) ) . In this paper, we compute the 𝑁 𝑘 -polynomial of all graphs of order 𝑛 ≤ 6 , and present it in a table. The complement graph of every graph is found and presented directly in the same row of the table. Moreover, the roots 𝑍 ( 𝑘 ( 𝐺 , 𝑥 ) ) of every 𝑁 𝑘 -polynomial are estimated. The classes of graphs with the same 𝑁 𝑘 -polynomial are found. Finally, the relationship between the coefficients of 𝑁 𝑘 - polynomial and graph connectivity is presented.
ISSN: 2709-9695

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