Cayley Properties of the Line Graphs Induced by Consecutive Layers of the Hypercube

Mirafzal, S. Morteza

doi:10.1007/s40840-020-01009-3

Cited by 15 publications

(19 citation statements)

References 23 publications

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“…The bipartite Kneser graph H(n, 1) has V as its vertex-set, and two vertices v, w are adjacent if and only if v ⊂ w or w ⊂ v. It is easy to see that H(n, 1) is a bipartite graph of diameter 3. Some of properties of the graph H(n, 1) and a generalization of it have been appeared in [11,13,14]. We can easyly show that H(n, 1) is a design graph with parameters (n, n − 1, n − 2).…”

Section: Introductionmentioning

confidence: 92%

On the distance eigenvalues of design graphs

Mirafzal¹

2021

Preprint

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A design graph is a regular bipartite graph in which any two distinct vertices of the same part have the same number of common neighbors. This class of graphs have a close relationship to strongly regular graphs. In this paper, we study the distance eigenvalues of the design graphs. Also, we will explicitly determine the distance eigenvalues of a class of design graphs, and determine the values for which the class is distance integral, that is, its distance eigenvalues are integers.

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Section: Introductionmentioning

confidence: 92%

On the distance eigenvalues of design graphs

Mirafzal¹

2021

Preprint

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“…. , n}, in which two vertices v and w are adjacent if and only if v ⊂ w or w ⊂ v. Recently, this class of graphs has been studied form several aspects [9,11,12,13]. It is easy to see that the crown graph Cr(n) is isomorphic with the bipartite graph H(n, 1).…”

Section: Introductionmentioning

confidence: 99%

The line graph of the crown graph is distance integral

Mirafzal¹

2021

Preprint

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The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D(G). A graph is called distance integral if all of its distance eigenvalues are integers. Let n ≥ 3 be an integer. A crown graph Cr(n) is a graph obtained from the complete bipartite graph K n,n by removing a perfect matching. Let L(Cr(n)) denote the line graph of the crown graph Cr(n). In this paper, by using the orbit partition method in algebraic graph theory, we determine the set of all distance eigenvalues of L(Cr(n)) and show that this graph is distance integral.

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“…Hence when n = 3, L(n) is the cycle C 6 . It can easily be seen that the graph B(n) is an edge-transitive graph [8], thus L(n) is a vertex-transitive graph [3,4]. The graph L(n) has some interesting properties and has been studied in some aspects [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…It can easily be seen that the graph B(n) is an edge-transitive graph [8], thus L(n) is a vertex-transitive graph [3,4]. The graph L(n) has some interesting properties and has been studied in some aspects [6,7,8]. In [8] it has been shown that the graph L(n) is a Cayley graph if and only if n is a power of a prime.…”

Section: Introductionmentioning

confidence: 99%

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$L(n)$ graphs are vertex-pancyclic and Hamilton-connected

Mirafzal¹,

Kouhi²

2021

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A graph G of order n > 2 is pancyclic if G contains a cycle of length l for each integer l with 3 ≤ l ≤ n and it is called vertex-pancyclic if every vertex is contained in a cycle of length l for every 3 ≤ l ≤ n. A graph G of order n > 2 is Hamilton-connected if for any pair of distinct vertices u and v, there is a Hamilton u-v path, namely, there is a u-v path of length n − 1. The graph B(n) is a graph with the vertex setIn this paper, we show that the graph L(n) is vertex-pancyclic and Hamilton-connected whenever n ≥ 6.

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Cayley Properties of the Line Graphs Induced by Consecutive Layers of the Hypercube

Cited by 15 publications

References 23 publications

On the distance eigenvalues of design graphs

On the distance eigenvalues of design graphs

The line graph of the crown graph is distance integral

$L(n)$ graphs are vertex-pancyclic and Hamilton-connected

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