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## Computing the zero forcing number for generalized Petersen graphs

#### Saeedeh RASHİDİ  , Nosratollah SHAJAREH POURSALAVATI  , Maryam TAVAKKOLI 

Let $G$ be a simple undirected graph with each vertex colored either white or black, $u$ be a black vertex of $G,$ and exactly one neighbor $v$ of $u$ be white. Then change the color of $v$ to black. When this rule is applied, we say $u$ forces $v,$ and write $u \rightarrow v$. A $zero\ forcing\ set$ of a graph $G$ is a subset $Z$ of vertices such that if initially the vertices in $Z$ are colored black and remaining vertices are colored white, the entire graph $G$ may be colored black by repeatedly applying the color-change rule. The zero forcing number of $G$, denoted $Z(G),$ is the minimum size of a zero forcing set.\\ In this paper, we investigate the zero forcing number for the generalized Petersen graphs (It is denoted by $P(n,k)$). We obtain upper and lower bounds for the zero forcing number for $P(n,k)$. We show that $Z(P(n,2))=6$ for $n\geq 10$, $Z(P(n,3))=8$ for $n\geq 12$ and $Z(P(2k+1,k))=6$ for $k\geq 5$.
Zero forcing number, Generalized Petersen graph, Colin de Verdi\{e}re parameter
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Primary Language en Engineering Articles Orcid: 0000-0002-8262-0910Author: Saeedeh RASHİDİ Institution: Shahid Bahonar University of KermanCountry: Iran Orcid: 0000-0003-0046-0325Author: Nosratollah SHAJAREH POURSALAVATI Institution: Shahid Bahonar University of KermanCountry: Iran Orcid: 0000-0002-2863-4799Author: Maryam TAVAKKOLI Institution: Shahid Bahonar University of KermanCountry: Iran This work was supported by Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran. Publication Date : May 7, 2020
 Bibtex @research article { jacodesmath729465, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {183 - 193}, doi = {10.13069/jacodesmath.729465}, title = {Computing the zero forcing number for generalized Petersen graphs}, key = {cite}, author = {Rashi̇di̇, Saeedeh and Shajareh Poursalavatı, Nosratollah and Tavakkolı, Maryam} }` APA Rashi̇di̇, S , Shajareh Poursalavatı, N , Tavakkolı, M . (2020). Computing the zero forcing number for generalized Petersen graphs . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (2) , 183-193 . DOI: 10.13069/jacodesmath.729465 MLA Rashi̇di̇, S , Shajareh Poursalavatı, N , Tavakkolı, M . "Computing the zero forcing number for generalized Petersen graphs" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 183-193 Chicago Rashi̇di̇, S , Shajareh Poursalavatı, N , Tavakkolı, M . "Computing the zero forcing number for generalized Petersen graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 183-193 RIS TY - JOUR T1 - Computing the zero forcing number for generalized Petersen graphs AU - Saeedeh Rashi̇di̇ , Nosratollah Shajareh Poursalavatı , Maryam Tavakkolı Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.729465 DO - 10.13069/jacodesmath.729465 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 183 EP - 193 VL - 7 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.729465 UR - https://doi.org/10.13069/jacodesmath.729465 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Computing the zero forcing number for generalized Petersen graphs %A Saeedeh Rashi̇di̇ , Nosratollah Shajareh Poursalavatı , Maryam Tavakkolı %T Computing the zero forcing number for generalized Petersen graphs %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 2 %R doi: 10.13069/jacodesmath.729465 %U 10.13069/jacodesmath.729465 ISNAD Rashi̇di̇, Saeedeh , Shajareh Poursalavatı, Nosratollah , Tavakkolı, Maryam . "Computing the zero forcing number for generalized Petersen graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 2 (May 2020): 183-193 . https://doi.org/10.13069/jacodesmath.729465 AMA Rashi̇di̇ S , Shajareh Poursalavatı N , Tavakkolı M . Computing the zero forcing number for generalized Petersen graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(2): 183-193. Vancouver Rashi̇di̇ S , Shajareh Poursalavatı N , Tavakkolı M . Computing the zero forcing number for generalized Petersen graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(2): 183-193.

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