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## The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$

#### Maryam Rahmani Moghaddam [1] , Kewen Zhao [2] , Sara Pouyandeh [3] , Ali Zeydi Abdian [4]

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Characterizing classes of graphs which are determined by their spectra is often a hard and challenging problem. So, finding and introducing any class of these graphs can be an interesting and important problem. This paper aims to characterize new classes of multicone graphs which are determined by both their adjacency spectra and their Laplacian spectra. A multicone graph is obtained from the join of a clique and a regular graph. Let $K_w$ be a complete graph on $w$ vertices. It is proved that multicone graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$ are determined by both their adjacency spectra and their Laplacian spectra, where $P_{17}$ and $S$ denote Paley graph of order 17 and Schlafli graph, respectively.
Adjacency spectrum, Laplacian spectrum, Multicone graph, Paley graph of order 17, DS graph, Schlafli graph
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Primary Language en Engineering Articles Author: Maryam Rahmani Moghaddam Author: Kewen Zhao (Primary Author) Author: Sara Pouyandeh Author: Ali Zeydi Abdian (Primary Author)Institution: Lorestan UniversityCountry: Iran Publication Date: April 15, 2019
 Bibtex @research article { konuralpjournalmath412927, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2019}, volume = {7}, pages = {192 - 198}, doi = {}, title = {The Spectral Determinations of the Multicone Graphs \$K\_w\\bigtriangledown P\_\{17\}\\bigtriangledown P\_\{17\} \$ and \$K\_w\\bigtriangledown S\\bigtriangledown S\$}, key = {cite}, author = {Rahmani Moghaddam, Maryam and Zhao, Kewen and Pouyandeh, Sara and Zeydi Abdian, Ali} } APA Rahmani Moghaddam, M , Zhao, K , Pouyandeh, S , Zeydi Abdian, A . (2019). The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$. Konuralp Journal of Mathematics (KJM), 7 (1), 192-198. Retrieved from http://dergipark.org.tr/konuralpjournalmath/issue/31492/412927 MLA Rahmani Moghaddam, M , Zhao, K , Pouyandeh, S , Zeydi Abdian, A . "The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$". Konuralp Journal of Mathematics (KJM) 7 (2019): 192-198 Chicago Rahmani Moghaddam, M , Zhao, K , Pouyandeh, S , Zeydi Abdian, A . "The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$". Konuralp Journal of Mathematics (KJM) 7 (2019): 192-198 RIS TY - JOUR T1 - The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$ AU - Maryam Rahmani Moghaddam , Kewen Zhao , Sara Pouyandeh , Ali Zeydi Abdian Y1 - 2019 PY - 2019 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 192 EP - 198 VL - 7 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2019 ER - EndNote %0 Konuralp Journal of Mathematics (KJM) The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$ %A Maryam Rahmani Moghaddam , Kewen Zhao , Sara Pouyandeh , Ali Zeydi Abdian %T The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$ %D 2019 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 7 %N 1 %R %U ISNAD Rahmani Moghaddam, Maryam , Zhao, Kewen , Pouyandeh, Sara , Zeydi Abdian, Ali . "The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$". Konuralp Journal of Mathematics (KJM) 7 / 1 (April 2019): 192-198. AMA Rahmani Moghaddam M , Zhao K , Pouyandeh S , Zeydi Abdian A . The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$. Konuralp J. Math.. 2019; 7(1): 192-198. Vancouver Rahmani Moghaddam M , Zhao K , Pouyandeh S , Zeydi Abdian A . The Spectral Determinations of the Multicone Graphs $K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $K_w\bigtriangledown S\bigtriangledown S$. Konuralp Journal of Mathematics (KJM). 2019; 7(1): 198-192.