Note on the spectral characterization of some cubic graphs with maximum number of triangles

Liu, Fenjin; Huang, Qiongxiang; Lai, Hsin-Hua

doi:10.1016/j.laa.2012.09.015

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…In [36], it have been shown that this graph is also DQS. Remark 5 Some 3-regular DAS graphs are given in [31,43]. We can obtain DQS graphs with independent edges and isolated vertices and isolated vertices from Corollary 3.4.…”

Section: Resultsmentioning

confidence: 99%

Graphs determined by signless Laplacian spectra

Abdian

Behmaram

Fath-Tabar

2020

AKCE International Journal of Graphs and Combinatorics

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In the past decades, graphs that are determined by their spectrum have received more attention, since they have been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. An important part of spectral graph theory is devoted to determining whether given graphs or classes of graphs are determined by their spectra or not. So, finding and introducing any class of graphs which are determined by their spectra can be an interesting and important problem. A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph G, we show that G ∪ rK1 ∪ sK2 is DQS under certain conditions, where r, s are natural numbers and K1 and K2 denote the complete graphs on one vertex and two vertices, respectively. Applying these results, some DQS graphs with independent edges and isolated vertices are obtained.

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Section: Resultsmentioning

confidence: 99%

Graphs determined by signless Laplacian spectra

Abdian

Behmaram

Fath-Tabar

2020

AKCE International Journal of Graphs and Combinatorics

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“…Remark 3.5. Some 3-regular DS graphs are given in [9,14,25]. We can obtain DQS graphs with isolated vertices from Theorem 3.13.…”

Section: Theorem 32mentioning

confidence: 99%

Signless Laplacian spectral characterization of graphs with isolated vertices

Huang

Zhou

2016

Filomat

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Laplacian spectral characterization of dumbbell graphs and theta graphs

Liu

2016

Discrete Math. Algorithm. Appl.

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Let $P_n$ and $C_n$ denote the path and cycle on $n$ vertices respectively. The dumbbell graph, denoted by $D_{p,k,q}$, is the graph obtained from two cycles $C_p$, $C_q$ and a path $P_{k+2}$ by identifying each pendant vertex of $P_{k+2}$ with a vertex of a cycle respectively. The theta graph, denoted by $\Theta_{r,s,t}$, is the graph formed by joining two given vertices via three disjoint paths $P_{r}$, $P_{s}$ and $P_{t}$ respectively. In this paper, we prove that all dumbbell graphs as well as theta graphs are determined by their Laplacian spectra

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Note on the spectral characterization of some cubic graphs with maximum number of triangles

Abstract: Cubic graphs of given order with maximum number of triangles are characterized. Consequently, it is proved that certain cubic graphs with maximum number of triangles are determined by their adjacency spectrum.

Cited by 3 publications

References 15 publications

Graphs determined by signless Laplacian spectra

Graphs determined by signless Laplacian spectra

Signless Laplacian spectral characterization of graphs with isolated vertices

Laplacian spectral characterization of dumbbell graphs and theta graphs

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