A study on deg-centric graphs

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-6174

Keywords:

Distance, eccentricity, deg-centric graphs, $D$-completable graphs

Abstract

The deg-centric graph of a simple, connected graph $G$, denoted by $G_d$, is a graph constructed from $G$ such that, $V(G_d) = V(G)$ and $E(G_d) = \{v_iv_j: d_G(v_i,v_j) \leq deg_G(v_i)\}$. In this paper, the concepts of deg-centric graphs and iterated deg-centrication of a graph are introduced and discussed.

References

J. A. K. Ando and D. Avis. Eccentric graphs. Discrete Mathematics, 56(1):1–6, 1985.

G. Chartrand, W. Gu, M. Schultz, and S. J. Winters. Eccentric graphs. Networks: An International Journal, 34(2):115–121, 1999.

R. Gould. Graph theory. Courier Corporation, 2012.

I. Gutman. Distance of thorny graphs. Publ. Inst. Math.(Beograd), 63(31-36):73–74, 1998.

S. Kaspar, B. Gayathri, M. Kulandaivel, and N. Shobhanadevi. Eccentric graphs of some particular classes of graphs. Int J Pure Appl Math, 16:145–152, 2018.

M. R. Raja, T. A. Mangam, and S. Naduvath. Eccentric completion of a graph. Communications in Combinatorics and Optimization, 7(2):193–201, 2022.

D. B. West et al. Introduction to graph theory, volume 2. Prentice hall Upper Saddle River, 2001.

P. Zhang and G. Chartrand. Introduction to graph theory. Tata McGraw-Hill, 2006.

Published

2024-06-24

How to Cite

[1]
S. Naduvath, T. T. Thalavayalil, and J. . Kok, “A study on deg-centric graphs”, Proyecciones (Antofagasta, On line), vol. 43, no. 4, pp. 911-926, Jun. 2024.

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Section

Artículos