scholarly journals Hamming dimension of a graph—The case of Sierpiński graphs

2013 ◽  
Vol 34 (2) ◽  
pp. 460-473 ◽  
Author(s):  
Sandi Klavžar ◽  
Iztok Peterin ◽  
Sara Sabrina Zemljič
Keyword(s):  
Sierpiński Graphs

scholarly journals On distances in Sierpiński graphs: Almost-extreme vertices and metric dimension

2013 ◽  
Vol 7 (1) ◽  
pp. 72-82 ◽  
Author(s):  
Sandi Klavzar ◽  
Sara Zemljic
Keyword(s):  
Computer Science ◽  
Metric Dimension ◽  
Fractal Nature ◽  
Explicit Formulas ◽  
Arbitrary Vertex ◽  
Tower Of Hanoi ◽  
Sierpiński Graphs ◽  
Total Distance

Sierpi?ski graphs Sn p form an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. An almost-extreme vertex of Sn p is introduced as a vertex that is either adjacent to an extreme vertex of Sn p or is incident to an edge between two subgraphs of Sn p isomorphic to Snp-1. Explicit formulas are given for the distance in Sn p between an arbitrary vertex and an almostextreme vertex. The formulas are applied to compute the total distance of almost-extreme vertices and to obtain the metric dimension of Sierpi?ski graphs.

scholarly journals Zeros of the Potts model partition function on Sierpinski graphs

2013 ◽  
Vol 377 (9) ◽  
pp. 671-675 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Robert Shrock
Keyword(s):  
Partition Function ◽  
Potts Model ◽  
Sierpiński Graphs

The 2-Rainbow Domination of Sierpiński Graphs and Extended Sierpiński Graphs

2017 ◽  
Vol 61 (3) ◽  
pp. 893-906 ◽  
Author(s):  
Jia-Jie Liu ◽  
Shun-Chieh Chang ◽  
Chiou-Jiun Lin
Keyword(s):  
Sierpiński Graphs ◽  
Extended Sierpiński Graphs ◽  
Rainbow Domination

scholarly journals On distances in generalized Sierpiński graphs

2018 ◽  
Vol 12 (1) ◽  
pp. 49-69 ◽  
Author(s):  
Alejandro Estrada-Moreno ◽  
Erick Rodríguez-Bazan ◽  
Juan Rodríguez-Velázquez
Keyword(s):  
Explicit Formula ◽  
Recursive Formula ◽  
Arbitrary Vertex ◽  
Base Graph ◽  
Sierpiński Graphs ◽  
Recursive Formulas

In this paper we propose formulas for the distance between vertices of a generalized Sierpi?ski graph S(G, t) in terms of the distance between vertices of the base graph G. In particular, we deduce a recursive formula for the distance between an arbitrary vertex and an extreme vertex of S(G, t), and we obtain a recursive formula for the distance between two arbitrary vertices of S(G, t) when the base graph is triangle-free. From these recursive formulas, we provide algorithms to compute the distance between vertices of S(G, t). In addition, we give an explicit formula for the diameter and radius of S(G, t) when the base graph is a tree.

Italian domination on Mycielskian and Sierpinski graphs

2020 ◽  
pp. 2150037
Author(s):  
Jismy Varghese ◽  
S. Aparna Lakshmanan
Keyword(s):  
Minimum Weight ◽  
Domination Number ◽  
Sierpiński Graphs ◽  
Number Formula ◽  
Sum Formula ◽  
The Impact ◽  
Edge Addition ◽  
Dominating Function

An Italian dominating function (IDF) of a graph G is a function [Formula: see text] satisfying the condition that for every [Formula: see text] with [Formula: see text] The weight of an IDF on [Formula: see text] is the sum [Formula: see text] and Italian domination number, [Formula: see text] is the minimum weight of an IDF. In this paper, we prove that [Formula: see text] where [Formula: see text] is the Mycielskian graph of [Formula: see text]. We have also studied the impact of edge addition on Italian domination number. We also obtain a bound for the Italian domination number of Sierpinski graph [Formula: see text] and find the exact value of [Formula: see text].

Hitting Times for Random Walks on Sierpiński Graphs and Hierarchical Graphs

2020 ◽  
Vol 63 (9) ◽  
pp. 1385-1396
Author(s):  
Yi Qi ◽  
Yuze Dong ◽  
Zhongzhi Zhang ◽  
Zhang Zhang
Keyword(s):  
Random Walks ◽  
Local Area Networks ◽  
Structural Difference ◽  
Local Area ◽  
Hitting Times ◽  
Topological Properties ◽  
Sierpiński Graphs ◽  
Model Complex ◽  
Self Similar ◽  
Processing Architectures

Abstract The Sierpiński graphs and hierarchical graphs are two much studied self-similar networks, both of which are iteratively constructed and have the same number of vertices and edges at any iteration, but display entirely different topological properties. Both graphs have a large variety of applications: Sierpiński graphs have a close connection with WK-recursive networks that are employed extensively in the design and implementation of local area networks and parallel processing architectures, while hierarchical graphs can be used to model complex networks. In this paper, we study hitting times for several absorbing random walks in Sierpiński graphs and hierarchical graphs. For all considered random walks, we determine exact solutions to hitting times for both graphs. The obtained explicit expressions indicate that the hitting times in both graphs behave quite differently. We show that the structural difference of the graphs is responsible for the disparate behaviors of their hitting times.

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