Pub Date : 2023-09-04DOI: 10.26493/2590-9770.1573.7b1
Yaser Rowshan, M. Gholami
{"title":"Multipartite Ramsey number of complete graphs versus matchings","authors":"Yaser Rowshan, M. Gholami","doi":"10.26493/2590-9770.1573.7b1","DOIUrl":"https://doi.org/10.26493/2590-9770.1573.7b1","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"7 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69338939","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 : 2023-08-01DOI: 10.26493/2590-9770.1575.f8d
R. Nedela, Jozef Širáň
{"title":"Half-arc-transitive graphs of arbitrarily large girth","authors":"R. Nedela, Jozef Širáň","doi":"10.26493/2590-9770.1575.f8d","DOIUrl":"https://doi.org/10.26493/2590-9770.1575.f8d","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47948727","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 : 2023-07-11DOI: 10.26493/2590-9770.1645.d36
T. Goy, M. Shattuck
{"title":"Determinant identities for the Catalan, Motzkin and Schröder numbers","authors":"T. Goy, M. Shattuck","doi":"10.26493/2590-9770.1645.d36","DOIUrl":"https://doi.org/10.26493/2590-9770.1645.d36","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49314641","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 : 2023-06-27DOI: 10.26493/2590-9770.1658.c96
B. Freyberg
{"title":"On face-magic labelings of regular tesselations","authors":"B. Freyberg","doi":"10.26493/2590-9770.1658.c96","DOIUrl":"https://doi.org/10.26493/2590-9770.1658.c96","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49207827","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 : 2023-04-12DOI: 10.26493/2590-9770.1644.9ac
S. Fried, T. Mansour
We initiate the study of what we refer to as random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that the labeling occurs increasingly whenever an unlabeled vertex is encountered. Some of the results we obtain involve sums of inverses of binomial coefficients, for which we obtain new identities. In particular, we prove that $sum_{k=0}^{n-1}2^{k}(2k+1)^{-1}binom{2k}{k}^{-1}binom{n+k}{k}=binom{2n}{n}2^{-n}sum_{k=0}^{n-1}2^{k}(2k+1)^{-1}binom{2k}{k}^{-1}$, thus confirming a conjecture of Bala.
{"title":"Graph labelings obtainable by random walks","authors":"S. Fried, T. Mansour","doi":"10.26493/2590-9770.1644.9ac","DOIUrl":"https://doi.org/10.26493/2590-9770.1644.9ac","url":null,"abstract":"We initiate the study of what we refer to as random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that the labeling occurs increasingly whenever an unlabeled vertex is encountered. Some of the results we obtain involve sums of inverses of binomial coefficients, for which we obtain new identities. In particular, we prove that $sum_{k=0}^{n-1}2^{k}(2k+1)^{-1}binom{2k}{k}^{-1}binom{n+k}{k}=binom{2n}{n}2^{-n}sum_{k=0}^{n-1}2^{k}(2k+1)^{-1}binom{2k}{k}^{-1}$, thus confirming a conjecture of Bala.","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"7 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69338995","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 : 2023-04-05DOI: 10.26493/2590-9770.1639.4c9
M. Changat, Prasanth G. Narasimha-Shenoi, Mary Shalet Thottungal Joseph
{"title":"Center and periphery of lexicographic product of digraphs","authors":"M. Changat, Prasanth G. Narasimha-Shenoi, Mary Shalet Thottungal Joseph","doi":"10.26493/2590-9770.1639.4c9","DOIUrl":"https://doi.org/10.26493/2590-9770.1639.4c9","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44626579","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 : 2023-03-14DOI: 10.26493/2590-9770.1632.16d
V. P. Korzhik
{"title":"All 2-planar graphs having the same spanning subgraph","authors":"V. P. Korzhik","doi":"10.26493/2590-9770.1632.16d","DOIUrl":"https://doi.org/10.26493/2590-9770.1632.16d","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"24 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69338991","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 : 2023-01-26DOI: 10.26493/2590-9770.1598.e49
H. Prodinger
{"title":"Skew Dyck paths without up-down-left","authors":"H. Prodinger","doi":"10.26493/2590-9770.1598.e49","DOIUrl":"https://doi.org/10.26493/2590-9770.1598.e49","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"7 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69338947","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 : 2023-01-13DOI: 10.26493/2590-9770.1613.15d
D. Morris
The Cartesian product of two cycles (of length m and length n) has a natural embedding on the torus, such that each face of the embedding is a 4-cycle. The toroidal grid Qd(m,n,r) is a generalization of this in which there is a shift by r when traversing the meridian of length m. In 2008, Steve Wilson found two interesting infinite families of (nonbipartite) toroidal grids that are unstable. (By definition, this means that the canonical bipartite double cover of the grid has more than twice as many automorphisms as the grid has.) It is easy to see that bipartite grids are also unstable, because the canonical double cover is disconnected. Furthermore, there are degenerate cases in which there exist two different vertices that have the same neighbours. This paper proves Wilson's conjecture that Qd(m,n,r) is stable for all other values of the parameters. In addition, we prove an analogous conjecture of Wilson for the triangular grids Tr(m,n,r) that are obtained by adding a diagonal to each face of Qd(m,n,r) (with all of the added diagonals parallel to each other).
{"title":"Automorphisms of the canonical double cover of a toroidal grid","authors":"D. Morris","doi":"10.26493/2590-9770.1613.15d","DOIUrl":"https://doi.org/10.26493/2590-9770.1613.15d","url":null,"abstract":"The Cartesian product of two cycles (of length m and length n) has a natural embedding on the torus, such that each face of the embedding is a 4-cycle. The toroidal grid Qd(m,n,r) is a generalization of this in which there is a shift by r when traversing the meridian of length m. In 2008, Steve Wilson found two interesting infinite families of (nonbipartite) toroidal grids that are unstable. (By definition, this means that the canonical bipartite double cover of the grid has more than twice as many automorphisms as the grid has.) It is easy to see that bipartite grids are also unstable, because the canonical double cover is disconnected. Furthermore, there are degenerate cases in which there exist two different vertices that have the same neighbours. This paper proves Wilson's conjecture that Qd(m,n,r) is stable for all other values of the parameters. In addition, we prove an analogous conjecture of Wilson for the triangular grids Tr(m,n,r) that are obtained by adding a diagonal to each face of Qd(m,n,r) (with all of the added diagonals parallel to each other).","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45144067","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 : 2023-01-12DOI: 10.26493/2590-9770.1550.f59
Joy Morris, Adrian Skelton
{"title":"Cayley graphs on abelian and generalized dihedral groups","authors":"Joy Morris, Adrian Skelton","doi":"10.26493/2590-9770.1550.f59","DOIUrl":"https://doi.org/10.26493/2590-9770.1550.f59","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45577249","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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