The spectral determinations of the connected multicone graphs K w ▽ m P 17 and K w ▽ m S

Ali Zeydi Abdian; S. Morteza Mirafzal

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 4, page 1091-1104
  • ISSN: 0011-4642

Abstract

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Finding and discovering any class of graphs which are determined by their spectra is always an important and interesting problem in the spectral graph theory. The main aim of this study is to characterize two classes of multicone graphs which are determined by both their adjacency and Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let K w denote a complete graph on w vertices, and let m be a positive integer number. In A. Z. Abdian (2016) it has been shown that multicone graphs K w ▽ P 17 and K w ▽ S are determined by both their adjacency and Laplacian spectra, where P 17 and S denote the Paley graph of order 17 and the Schläfli graph, respectively. In this paper, we generalize these results and we prove that multicone graphs K w ▽ m P 17 and K w ▽ m S are determined by their adjacency spectra as well as their Laplacian spectra.

How to cite

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Abdian, Ali Zeydi, and Mirafzal, S. Morteza. "The spectral determinations of the connected multicone graphs $ K_w\bigtriangledown mP_{17} $ and $ K_w\bigtriangledown mS $." Czechoslovak Mathematical Journal 68.4 (2018): 1091-1104. <http://eudml.org/doc/294845>.

@article{Abdian2018,
abstract = {Finding and discovering any class of graphs which are determined by their spectra is always an important and interesting problem in the spectral graph theory. The main aim of this study is to characterize two classes of multicone graphs which are determined by both their adjacency and Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let $ K_w $ denote a complete graph on $ w $ vertices, and let $ m $ be a positive integer number. In A. Z. Abdian (2016) it has been shown that multicone graphs $ K_w\bigtriangledown P_\{17\}$ and $ K_w\bigtriangledown S$ are determined by both their adjacency and Laplacian spectra, where $ P_\{17\} $ and $ S$ denote the Paley graph of order 17 and the Schläfli graph, respectively. In this paper, we generalize these results and we prove that multicone graphs $ K_w\bigtriangledown mP_\{17\}$ and $ K_w\bigtriangledown mS$ are determined by their adjacency spectra as well as their Laplacian spectra.},
author = {Abdian, Ali Zeydi, Mirafzal, S. Morteza},
journal = {Czechoslovak Mathematical Journal},
keywords = {DS (determined by spectrum) graph; Schläfli graph; multicone graph; adjacency spectrum; Laplacian spectrum; Paley graph of order 17},
language = {eng},
number = {4},
pages = {1091-1104},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The spectral determinations of the connected multicone graphs $ K_w\bigtriangledown mP_\{17\} $ and $ K_w\bigtriangledown mS $},
url = {http://eudml.org/doc/294845},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Abdian, Ali Zeydi
AU - Mirafzal, S. Morteza
TI - The spectral determinations of the connected multicone graphs $ K_w\bigtriangledown mP_{17} $ and $ K_w\bigtriangledown mS $
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 1091
EP - 1104
AB - Finding and discovering any class of graphs which are determined by their spectra is always an important and interesting problem in the spectral graph theory. The main aim of this study is to characterize two classes of multicone graphs which are determined by both their adjacency and Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let $ K_w $ denote a complete graph on $ w $ vertices, and let $ m $ be a positive integer number. In A. Z. Abdian (2016) it has been shown that multicone graphs $ K_w\bigtriangledown P_{17}$ and $ K_w\bigtriangledown S$ are determined by both their adjacency and Laplacian spectra, where $ P_{17} $ and $ S$ denote the Paley graph of order 17 and the Schläfli graph, respectively. In this paper, we generalize these results and we prove that multicone graphs $ K_w\bigtriangledown mP_{17}$ and $ K_w\bigtriangledown mS$ are determined by their adjacency spectra as well as their Laplacian spectra.
LA - eng
KW - DS (determined by spectrum) graph; Schläfli graph; multicone graph; adjacency spectrum; Laplacian spectrum; Paley graph of order 17
UR - http://eudml.org/doc/294845
ER -

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