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Dergiler / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2019 / Cilt: 9 - Sayı: 1

ON TOTAL VERTEX-EDGE DOMINATION

Bünyamin ŞAHİN
Abdulgani ŞAHİN
Sayfa
128–133
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Furthermore we provide a characterization of trees T with γ t ve(T) = γ t (T).

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper we obtain an improved upper bound of total vertex edgedomination number of a tree.
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Temel Bulgular & Veri:If T is a connected tree with order n, then γ t ve(T) ≤ m 3 with m = 6d n 6 e and we characterize the trees attaining this upper bound.
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Sonuç & Katkı:Furthermore we provide a characterization of trees T with γ t ve(T) = γ t (T).
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Özet

In this paper we obtain an improved upper bound of total vertex edgedomination number of a tree. If T is a connected tree with order n, then γ t ve(T) ≤ m 3 with m = 6d n 6 e and we characterize the trees attaining this upper bound. Furthermore we provide a characterization of trees T with γ t ve(T) = γ t (T).

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Bu Makaleye Atıf Yap

ŞAHİN, B., ŞAHİN, A. (2019). ON TOTAL VERTEX-EDGE DOMINATION. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 9 - Sayı: 1, 128–133. https://ajindex.com/articles/341358

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Kaynakça (8)

  1. Boutrig, R. and Chellali, M., (in press), Total vertex-edge domination, International Journal of Computer Mathematics
  2. Boutrig, R., Chellali, M., Haynes, T. W. and Hedetniemi, S. T., (2016), Vertex-edge domination in graphs, Aequationes Mathematicae, 90(2), pp. 355-366
  3. Haynes, T. W., Hedetniemi, S. T. and Slater, P. J., (1998), Fundamentals of Domination in Graphs, Marcel Dekker, New York
  4. Kang, C. X., (2014), Total domination value in graphs, Util. Math., 95, pp. 263-279
  5. Krishnakumari, B., Venkatakrishnan, Y. B. and Krzywkowski, M., (2014), Bounds on the vertex-edge domination number, C.R. Acad. Sci. Paris, Ser. I 352, pp. 363-366
  6. Krishnakumari B., Venkatakrishnan Y. B. and Krzywkowski, M., (2016), On trees with total domination number equal to edge-vertex domination number plus one, Proc. Indian Acad. Sci. (Math. Sci.), 126(2), pp. 153-157
  7. Lewis, J. R., Hedetniemi, S. T., Haynes, T. W. and Fricke, G. H., (2010), Vertex-edge domination, Util. Math., 81, pp. 193213
  8. Peters, J. W., (1986), Theoretical and algorithmic results on domination and connectivity, Ph.D. thesis, Clemson University.