On distances in generalized Sierpinski graphs

Estrada‐Moreno, Alejandro; Rodríguez-Bazan, Erick D.; Rodríguez-Velázquez, Juan A.

doi:10.48550/arxiv.1608.00769

Cited by 1 publication

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“…They provide a total coloring for the WK-recursive topology, which also gives the tight bound. In [8] the distance between vertices of S(G, t) is expressed in terms of the distance between vertices of the base graph G. In addition, the authors give an explicit formula for the diameter and the radius of S(G, t) when the base graph G is a tree. In [34] their independence number, chromatic number, vertex cover number, clique number and domination number are investigated in terms of the similar parameters of the base graph G. The strong metric dimension of these graphs is studied in [7].…”

Section: Introductionmentioning

confidence: 99%

Degree sequence of the generalized Sierpinski graph

Behtoei,

Attarzadeh,

Khatibi

2019

Preprint

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The degree sequence of (ordinary) Sierpiński graphs and Hanoi graphs are determined in the literature. Also, In [ J.A. Rodriguez-Velázquez, E.D. Rodriguez-Bazan, A. Estrada-Moreno, On generalized Sierpiński graphs, Discuss. Math. Graph T., 37 (3), 2017, 547-560.] the authors determine the number of leaves (vertices of degree one) of the generalized Sierpiński S(T, t) of any tree T in terms of t, |V (T )| and the number of leaves of the base graph T . In this paper, among some other results, we generalize these results. More precisely, for every simple graph G of order n, we completely determine the degree sequence of the generalized Sierpiński graph S(G, t) of G in terms of n, t and the degree sequence of G. Also, we determine the exact value of the general first Zagreb index of S(G, t) in terms of the same parameters of G.

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Section: Introductionmentioning

confidence: 99%