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Hosseini pour, Seyedeh Maryam, Rahbarnia, Freydoon, Alaeiyan, Mehdi, Erfanian, Ahmad. (1399). On nicely distance-balanced of folded cube graphs. , 7(29), 117-128.
Seyedeh Maryam Hosseini pour; Freydoon Rahbarnia; Mehdi Alaeiyan; Ahmad Erfanian. "On nicely distance-balanced of folded cube graphs". , 7, 29, 1399, 117-128.
Hosseini pour, Seyedeh Maryam, Rahbarnia, Freydoon, Alaeiyan, Mehdi, Erfanian, Ahmad. (1399). 'On nicely distance-balanced of folded cube graphs', , 7(29), pp. 117-128.
Hosseini pour, Seyedeh Maryam, Rahbarnia, Freydoon, Alaeiyan, Mehdi, Erfanian, Ahmad. On nicely distance-balanced of folded cube graphs. , 1399; 7(29): 117-128.

On nicely distance-balanced of folded cube graphs

Journal of New Researches in Mathematics
مقاله 12، دوره 7، شماره 29، خرداد و تیر 2021، صفحه 117-128  XML اصل مقاله (1.87 M)
نوع مقاله: research paper
نویسندگان
Seyedeh Maryam Hosseini pour1؛ Freydoon Rahbarnia email 2؛ Mehdi Alaeiyan3؛ Ahmad Erfanian4
1Department of Pure Mathematics, Ferdowsi University of Mashhad,
2Department of Applied Mathematics, Ferdowsi University ofMashhad,
3School of Mathematic, Iran University of Science and Technology, Tehran, Iran.
4Department of Mathematics and Center of Excellence in Analysis on Algebraic Structure
چکیده
A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ_V (γ_E), such that for any adjacent vertices u and v in V(Γ), there are exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ) that are closer to u than v, and exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ)) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced.

A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ_V (γ_E), such that for any adjacent vertices u and v in V(Γ), there are exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ) that are closer to u than v, and exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ)) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced.
کلیدواژه‌ها
: nicely distance-balanced؛ nicely edge distance-balanced؛ hamming graph؛ hyper cube؛ folded cube
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