Pub Date : 2023-01-20DOI: 10.1142/s179383092350009x
Raúl M. Falcón, M. Venkatachalam, S. J. Margaret
{"title":"Solving the b-coloring problem for subdivision-edge neighbourhood coronas","authors":"Raúl M. Falcón, M. Venkatachalam, S. J. Margaret","doi":"10.1142/s179383092350009x","DOIUrl":"https://doi.org/10.1142/s179383092350009x","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"23 17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82943300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-20DOI: 10.1142/s1793830923500088
L. Boro, M. Singh
{"title":"Line graphs associated to Von Neumann regular graphs of rings","authors":"L. Boro, M. Singh","doi":"10.1142/s1793830923500088","DOIUrl":"https://doi.org/10.1142/s1793830923500088","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79646042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.1142/s1793830923500052
Biswaranjan Khanra, M. Mandal, Buddha Dev Ghosh
{"title":"On the power graph of a monogenic semigroup","authors":"Biswaranjan Khanra, M. Mandal, Buddha Dev Ghosh","doi":"10.1142/s1793830923500052","DOIUrl":"https://doi.org/10.1142/s1793830923500052","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"19 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82388738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-17DOI: 10.1142/s1793830923500040
Fahimeh Khosh-Ahang Ghasr
In this note, we generalize the concepts of (perfect) Roman and Italian dominations to (perfect) strong Roman and Roman k-domination for arbitrary positive integer k. These generalizations cover some of previous ones. After some comparison of their domination numbers, as a first study of these concepts, we study the (perfect, strong, perfect strong) Roman k-domination numbers of complete bipartite graphs.
{"title":"On a generalization of roman domination with more legions","authors":"Fahimeh Khosh-Ahang Ghasr","doi":"10.1142/s1793830923500040","DOIUrl":"https://doi.org/10.1142/s1793830923500040","url":null,"abstract":"In this note, we generalize the concepts of (perfect) Roman and Italian dominations to (perfect) strong Roman and Roman k-domination for arbitrary positive integer k. These generalizations cover some of previous ones. After some comparison of their domination numbers, as a first study of these concepts, we study the (perfect, strong, perfect strong) Roman k-domination numbers of complete bipartite graphs.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"35 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78014580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-25DOI: 10.1142/s1793830923500271
O. Egecioglu, Elif Saygı, Zülfükar Saygı
The diameter of a graph is the maximum distance between pairs of vertices in the graph. A pair of vertices whose distance is equal to its diameter are called diametrically opposite vertices. The collection of shortest paths between diametrically opposite vertices are referred as diametral paths. In this work, we enumerate the number of diametral paths for Fibonacci cubes, Lucas cubes and Alternate Lucas cubes. We present bijective proofs that show that these numbers are related to alternating permutations and are enumerated by Euler numbers.
{"title":"Euler Numbers and Diametral Paths in Fibonacci Cubes, Lucas Cubes and Alternate Lucas Cubes","authors":"O. Egecioglu, Elif Saygı, Zülfükar Saygı","doi":"10.1142/s1793830923500271","DOIUrl":"https://doi.org/10.1142/s1793830923500271","url":null,"abstract":"The diameter of a graph is the maximum distance between pairs of vertices in the graph. A pair of vertices whose distance is equal to its diameter are called diametrically opposite vertices. The collection of shortest paths between diametrically opposite vertices are referred as diametral paths. In this work, we enumerate the number of diametral paths for Fibonacci cubes, Lucas cubes and Alternate Lucas cubes. We present bijective proofs that show that these numbers are related to alternating permutations and are enumerated by Euler numbers.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"87 11 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87688743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-10DOI: 10.1142/s1793830923500490
Gerold Jager, F. Drewes
The AB~Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB~Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by placing a color from a set of $c$ colors on each of $p le c$ pegs, subject to the condition that every color is used at most once. The codebreaker tries to determine the secret by asking questions, where all questions are given at once and each question is a possible secret. As an answer the codemaker reveals the number of correctly placed colors for each of the questions. After that, the codebreaker only has one more try to determine the secret and thus to win the game. For given $p$ and $c$, our goal is to find the smallest number $k$ of questions the codebreaker needs to win, regardless of the secret, and the corresponding list of questions, called a $(k+1)$-strategy. We present a $lceil 4c/3 rceil-1)$-strategy for $p=2$ for all $c ge 2$, and a $lfloor (3c-1)/2 rfloor$-strategy for $p=3$ for all $c ge 4$ and show the optimality of both strategies, i.e., we prove that no $(k+1)$-strategy for a smaller $k$ exists.
AB游戏是一款类似于流行游戏《Mastermind》的游戏。我们研究了这个游戏的一个版本，叫做Static Black-Peg AB game。它由两个玩家，编码者和密码破译者来玩。编码者通过将一组$c$颜色中的一种颜色放在每个$p le c$标记上来创建一个所谓的秘密，但每种颜色最多只能使用一次。密码破译者试图通过提问来确定秘密，所有的问题都是一次给出的，每个问题都是一个可能的秘密。作为答案，编码人员会显示每个问题正确放置颜色的数量。在那之后，密码破译者只需要再尝试一次来确定密码，从而赢得游戏。对于给定的$p$和$c$，我们的目标是找到密码破译者需要赢得的最小问题数$k$，而不管秘密是什么，以及相应的问题列表，称为$(k+1)$ -策略。我们提出了针对所有$c ge 2$的$p=2$的$lceil 4c/3 rceil-1)$ -策略，以及针对所有$c ge 4$的$p=3$的$lfloor (3c-1)/2 rfloor$ -策略，并展示了这两种策略的最优性，即，我们证明了对于较小的$k$不存在$(k+1)$ -策略。
{"title":"Optimal Strategies for Static Black-Peg AB Game with Two and Three Pegs","authors":"Gerold Jager, F. Drewes","doi":"10.1142/s1793830923500490","DOIUrl":"https://doi.org/10.1142/s1793830923500490","url":null,"abstract":"The AB~Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB~Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by placing a color from a set of $c$ colors on each of $p le c$ pegs, subject to the condition that every color is used at most once. The codebreaker tries to determine the secret by asking questions, where all questions are given at once and each question is a possible secret. As an answer the codemaker reveals the number of correctly placed colors for each of the questions. After that, the codebreaker only has one more try to determine the secret and thus to win the game. For given $p$ and $c$, our goal is to find the smallest number $k$ of questions the codebreaker needs to win, regardless of the secret, and the corresponding list of questions, called a $(k+1)$-strategy. We present a $lceil 4c/3 rceil-1)$-strategy for $p=2$ for all $c ge 2$, and a $lfloor (3c-1)/2 rfloor$-strategy for $p=3$ for all $c ge 4$ and show the optimality of both strategies, i.e., we prove that no $(k+1)$-strategy for a smaller $k$ exists.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81651025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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