Hamiltonian character graphs

Ebrahimi, Mahdi; Iranmanesh, Ali; Hosseinzadeh, Mohammad Ali

doi:10.1016/j.jalgebra.2014.12.038

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…Suppose that G is a solvable group. In Theorem A of [4], the authors discussed a necessary and sufficient condition for ∆(G) to be Hamiltonian. They proved that ∆(G) is Hamiltonian if and only if it is a block with at least three vertices.…”

Section: Cut Vertices Of Character Graphsmentioning

confidence: 99%

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The influence of cut vertices and eigenvalues on character graphs of solvable groups

Hafezieh,

Hosseinzadeh,

Hossein-Zadeh

et al. 2019

Preprint

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Given a finite group G, the character graph, denoted by ∆(G), for its irreducible character degrees is a graph with vertex set ρ(G) which is the set of prime numbers that divide the irreducible character degrees of G, and with {p, q} being an edge if there exist a nonlinear χ ∈ Irr(G) whose degree is divisible by pq. In this paper, we discuss the influences of cut vertices and eigenvalues of ∆(G) on the group structure of G. Recently, Lewis and Meng proved the character graph of each solvable group has at most one cut vertex. Now, we determine the structure of character graphs of solvable groups with a cut vertex and diameter 3. Furthermore, we study solvable groups whose character graphs have at most two distinct eigenvalues. Moreover, we investigate the solvable groups whose character graphs are regular with three distinct eigenvalues. In addition, we give some lower bounds for the number of edges of ∆(G).

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Section: Cut Vertices Of Character Graphsmentioning

confidence: 99%

“…In [4], the authors discussed the necessary and sufficient conditions for ∆(G) to be Hamiltonian. As a graph with a cut vertex does not have a hamiltonian cycle, it is interesting to discuss the influence of such vertices on the structure of the graph ∆(G) and the structure of the group itself.…”

Section: Introductionmentioning

confidence: 99%

The influence of cut vertices and eigenvalues on character graphs of solvable groups

Hafezieh,

Hosseinzadeh,

Hossein-Zadeh

et al. 2019

Preprint

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“…We say that Γ is Hamiltonian if it contains a Hamilton cycle. In [2], it was shown that the character graph ∆(G) of a solvable group G is Hamiltonian if and only if ∆(G) is a block with at least three vertices. In this paper, we give a necessary and sufficient condition on the structure of a finite group G which guarantees that the complement of ∆(G) is a nonbipartite Hamiltonian graph.…”

Section: Introductionmentioning

confidence: 99%

Character Graphs With Nonbipartite Hamiltonian Complement

Ebrahimi¹

2019

Bull. Aust. Math. Soc.

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“…Sayanjali et.al [15] proved that the character graph ∆(G) of a finite group G is a connected regular graph of odd order, if and only if ∆(G) is complete. Also the character graph ∆(G) of a solvable group G is Hamiltonian if and only if ∆(G) is a block with at least 3 vertices [5]. We refer the readers to a survey by Lewis [9] for results concerning this graph and related topics.…”

Section: Introductionmentioning

confidence: 99%