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Mycielskian of graphs with small game domination number 具有小博弈支配数的图的Mycielskian
Art Discret. Appl. Math. Pub Date : 2022-02-01 DOI: 10.26493/2590-9770.1484.40e
Tijo James, A. Vijayakumar
{"title":"Mycielskian of graphs with small game domination number","authors":"Tijo James, A. Vijayakumar","doi":"10.26493/2590-9770.1484.40e","DOIUrl":"https://doi.org/10.26493/2590-9770.1484.40e","url":null,"abstract":"","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133793968","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}
引用次数: 0
On maximum Wiener index of directed grids 有向网格的最大Wiener指数
Art Discret. Appl. Math. Pub Date : 2022-01-28 DOI: 10.26493/2590-9770.1526.2b3
M. Knor, R. Škrekovski
{"title":"On maximum Wiener index of directed grids","authors":"M. Knor, R. Škrekovski","doi":"10.26493/2590-9770.1526.2b3","DOIUrl":"https://doi.org/10.26493/2590-9770.1526.2b3","url":null,"abstract":"This paper is devoted to Wiener index of directed graphs, more precisely of directed grids. The grid $G_{m,n}$ is the Cartesian product $P_mBox P_n$ of paths on $m$ and $n$ vertices, and in a particular case when $m=2$, it is a called the ladder graph $L_n$. Kraner v{S}umenjak et al. proved that the maximum Wiener index of a digraph, which is obtained by orienting the edges of $L_n$, is obtained when all layers isomorphic to one factor are directed paths directed in the same way except one (corresponding to an endvertex of the other factor) which is a directed path directed in the opposite way. Then they conjectured that the natural generalization of this orientation to $G_{m,n}$ will attain the maximum Wiener index among all orientations of $G_{m,n}$. In this paper we disprove the conjecture by showing that a comb-like orientation of $G_{m,n}$ has significiantly bigger Wiener index.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127834267","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}
引用次数: 0
Cyclotomic association schemes of broad classes and applications to the construction of combinatorial structures 广泛类别的环切关联方案及其在组合结构构造中的应用
Art Discret. Appl. Math. Pub Date : 2022-01-27 DOI: 10.26493/2590-9770.1436.0f3
Luis Martínez, María Asunción García, Leire Legarreta, I. Malaina
{"title":"Cyclotomic association schemes of broad classes and applications to the construction of combinatorial structures","authors":"Luis Martínez, María Asunción García, Leire Legarreta, I. Malaina","doi":"10.26493/2590-9770.1436.0f3","DOIUrl":"https://doi.org/10.26493/2590-9770.1436.0f3","url":null,"abstract":"In 2010, G. Fernández, R. Kwashira and L. Mart́ınez gave a new cyclotomy on A = ∏n i=1 Fqi , where Fqi is a finite field with qi elements. They defined a certain subgroup H of the group of units of this product ring A for which the quotient is cyclic. The orbits of the corresponding multiplicative action of the subgroup on the additive group of A are of two types: • The cyclotomic cosets of the quotient of the group of units of A over the subgroup H.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"51 1-3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116590876","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}
引用次数: 1
On the automorphisms of a family of small q-regular graphs of girth 8 周长为8的小q正则图族的自同构
Art Discret. Appl. Math. Pub Date : 2022-01-17 DOI: 10.26493/2590-9770.1425.1de
Stefan Gyürki, Pavol Jánoš
{"title":"On the automorphisms of a family of small q-regular graphs of girth 8","authors":"Stefan Gyürki, Pavol Jánoš","doi":"10.26493/2590-9770.1425.1de","DOIUrl":"https://doi.org/10.26493/2590-9770.1425.1de","url":null,"abstract":"","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131424882","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}
引用次数: 0
On distance signless Laplacian spectra of power graphs of the integer modulo group 整数模群幂图的距离无符号拉普拉斯谱
Art Discret. Appl. Math. Pub Date : 2022-01-13 DOI: 10.26493/2590-9770.1393.2be
B. Rather, S. Pirzada, T. A. Naikoo
{"title":"On distance signless Laplacian spectra of power graphs of the integer modulo group","authors":"B. Rather, S. Pirzada, T. A. Naikoo","doi":"10.26493/2590-9770.1393.2be","DOIUrl":"https://doi.org/10.26493/2590-9770.1393.2be","url":null,"abstract":"","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125136297","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}
引用次数: 6
Lexicographic palindromic products 词典回文产品
Art Discret. Appl. Math. Pub Date : 2022-01-04 DOI: 10.26493/2590-9770.1390.d21
Jamie Shive
{"title":"Lexicographic palindromic products","authors":"Jamie Shive","doi":"10.26493/2590-9770.1390.d21","DOIUrl":"https://doi.org/10.26493/2590-9770.1390.d21","url":null,"abstract":"","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"14 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126188207","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}
引用次数: 0
Number of colors needed to break symmetries of a graph by an arbitrary edge coloring 通过任意边着色打破图形对称性所需的颜色数
Art Discret. Appl. Math. Pub Date : 2021-11-14 DOI: 10.26493/2590-9770.1504.f7a
S. Alikhani, M. H. Shekarriz
{"title":"Number of colors needed to break symmetries of a graph by an arbitrary edge coloring","authors":"S. Alikhani, M. H. Shekarriz","doi":"10.26493/2590-9770.1504.f7a","DOIUrl":"https://doi.org/10.26493/2590-9770.1504.f7a","url":null,"abstract":"A coloring is distinguishing (or symmetry breaking) if no non-identity automorphism preserves it. The distinguishing threshold of a graph $G$, denoted by $theta(G)$, is the minimum number of colors $k$ so that every $k$-coloring of $G$ is distinguishing. We generalize this concept to edge-coloring by defining an alternative index $theta'(G)$. We consider $theta'$ for some families of graphs and find its connection with edge-cycles of the automorphism group. Then we show that $theta'(G)=2$ if and only if $Gsimeq K_{1,2}$ and $theta'(G)=3$ if and only if $Gsimeq P_4, K_{1,3}$ or $K_3$. Moreover, we prove some auxiliary results for graphs whose distinguishing threshold is 3 and show that although there are infinitely many such graphs, but they are not line graphs. Finally, we compute $theta'(G)$ when $G$ is the Cartesian product of simple prime graphs.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127472199","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}
引用次数: 0
Hole operations on Hurwitz maps 赫维茨地图上的钻孔操作
Art Discret. Appl. Math. Pub Date : 2021-11-10 DOI: 10.26493/2590-9770.1531.46a
G'abor G'evay, G. Jones
{"title":"Hole operations on Hurwitz maps","authors":"G'abor G'evay, G. Jones","doi":"10.26493/2590-9770.1531.46a","DOIUrl":"https://doi.org/10.26493/2590-9770.1531.46a","url":null,"abstract":"For a given group $G$ the orientably regular maps with orientation-preserving automorphism group $G$ are used as the vertices of a graph $O(G)$, with undirected and directed edges showing the effect of duality and hole operations on these maps. Some examples of these graphs are given, including several for small Hurwitz groups. For some $G$, such as the affine groups ${rm AGL}_1(2^e)$, the graph $O(G)$ is connected, whereas for some other infinite families, such as the alternating and symmetric groups, the number of connected components is unbounded.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"234 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124575855","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}
引用次数: 0
The graphs with a symmetrical Euler cycle 具有对称欧拉环的图
Art Discret. Appl. Math. Pub Date : 2021-11-04 DOI: 10.26493/2590-9770.1464.7cd
Jiyong Chen, Caiheng Li, C. Praeger, S. Song
{"title":"The graphs with a symmetrical Euler cycle","authors":"Jiyong Chen, Caiheng Li, C. Praeger, S. Song","doi":"10.26493/2590-9770.1464.7cd","DOIUrl":"https://doi.org/10.26493/2590-9770.1464.7cd","url":null,"abstract":"Dedicated to our friend and colleague Marston Conder on the occasion of his 65th birthday. The edges surrounding a face of a map M form a cycle C, called the boundary cycle of the face, and C is often not a simple cycle. If the map M is arc-transitive, then there is a cyclic subgroup of automorphisms of M which leaves C invariant and is bi-regular on the edges of the induced subgraph [C]; that is to say, C is a symmetrical Euler cycle of [C]. In this paper we determine the family of graphs (which may have multiple edges) whose edge-set can be sequenced to form a symmetrical Euler cycle. We first classify all graphs and which have a cyclic subgroup of automorphisms acting bi-regularly on edges. We then apply this classification to obtain the graphs possessing a symmetrical Euler cycle, and therefore are the (only) candidates for the induced subgraph of the boundary cycle of a face in an arc-transitive map.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132761612","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}
引用次数: 1
Deterministic bootstrap percolation on trees 树木上的确定性自举渗透
Art Discret. Appl. Math. Pub Date : 2021-10-14 DOI: 10.26493/2590-9770.1344.20c
R. Beeler, Rodney Keaton, F. Norwood
{"title":"Deterministic bootstrap percolation on trees","authors":"R. Beeler, Rodney Keaton, F. Norwood","doi":"10.26493/2590-9770.1344.20c","DOIUrl":"https://doi.org/10.26493/2590-9770.1344.20c","url":null,"abstract":"","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116054307","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}
引用次数: 0
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