On the k-distance differential of graphs
Künye
Mojdeh, A. & Masoumi, I. (2023). On the k-distance differential of graphs. TWMS Journal of Applied and Engineering Mathematics, 13(2), 614-625.Özet
Let G = (V, E) be a graph and X ? V . The differential of X is defined as ?(X) = |B(X)| ? |X| where B(X) is a set of all vertices in V ? X which has adjacent vertex in the set X. Also, the differential of a graph G written ?(G), is equal to max{?(X) : X ? V }. In this paper, we initiate the study of k-distance differential of graphs which is a generalization of differential of graphs. In addition, we show that for any connected graph G of order n ? k + 2, the number (2k?1)n / 2k+3 is a sharp lower bound for k-distance differential of G. We also obtain upper bounds for k-distance differential of graphs. Finally, we characterize the graphs whose k-distance differential belongs to {n ? 2, n ? 3, 1}.
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13Sayı
2Bağlantı
http://belgelik.isikun.edu.tr/xmlui/handle/iubelgelik/5487http://jaem.isikun.edu.tr/web/index.php/archive/119-vol13no2/994
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