| LEADER |
02310nam a22002417a 4500 |
| 001 |
2201534 |
| 041 |
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|a eng
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| 044 |
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|b اليمن
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| 100 |
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|9 771541
|a Naji, Ahmed M.
|e Author
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| 245 |
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|a An Atlas of K-Distance Neighborhood Polynomials of Graphs with at most Six Vertices
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| 260 |
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|b جامعة البيضاء
|c 2023
|g نوفمبر
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| 300 |
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|a 569 - 583
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| 336 |
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|a بحوث ومقالات
|b Article
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| 520 |
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|b 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.
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| 653 |
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|a المعادلات الرياضية
|a الرسوم البيانية
|a كثيرات الحدود
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| 692 |
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|b Second Degree (Of Vertex)
|b Distance
|b Graph Polynomial
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| 700 |
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|a Mahde, Sultan Senan
|e Co-Author
|9 698733
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| 773 |
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|c 046
|e AlBayda University Journal
|f Mağallaẗ ğāmiʿaẗ al-Bayḍāʾ li-l-buḥūṯ
|l 004
|m مج5, ع4
|o 2422
|s مجلة جامعة البيضاء
|v 005
|x 2709-9695
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| 856 |
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|u 2422-005-004-046.pdf
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| 930 |
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|d y
|p y
|q n
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| 995 |
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|a EduSearch
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| 995 |
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|a HumanIndex
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| 999 |
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|c 1456212
|d 1456212
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