Pub Date : 2023-01-01DOI: 10.20429/tag.2023.100111
O. Alomari, Mohammad Abudayah, Manal Ghanem
{"title":"The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs","authors":"O. Alomari, Mohammad Abudayah, Manal Ghanem","doi":"10.20429/tag.2023.100111","DOIUrl":"https://doi.org/10.20429/tag.2023.100111","url":null,"abstract":"","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545514","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 : 2023-01-01DOI: 10.20429/tag.2023.100201
Xiaofeng Wang, Taoye Zhang, Ju Zhou
Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular matroid M does not have a minor in {M((P10)¯3 ),M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)¯3 is the graph obtained from the Petersen graph P10by contracting 3 edges of a perfect matching. As both M(K3,3) and M(K5) are contractions of M((P10)¯3), our result extends the results of Walton and Welsh and Lai, Li and Poon.
{"title":"On Nowhere Zero 4-Flows in Regular Matroids","authors":"Xiaofeng Wang, Taoye Zhang, Ju Zhou","doi":"10.20429/tag.2023.100201","DOIUrl":"https://doi.org/10.20429/tag.2023.100201","url":null,"abstract":"Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular matroid M does not have a minor in {M((P10)¯3 ),M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)¯3 is the graph obtained from the Petersen graph P10by contracting 3 edges of a perfect matching. As both M(K3,3) and M(K5) are contractions of M((P10)¯3), our result extends the results of Walton and Welsh and Lai, Li and Poon.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135650136","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 : 2023-01-01DOI: 10.20429/tag.2023.100105
R. Jalaei, D. Mojdeh
{"title":"Outer Independent Double Italian Domination of Some Graph Products","authors":"R. Jalaei, D. Mojdeh","doi":"10.20429/tag.2023.100105","DOIUrl":"https://doi.org/10.20429/tag.2023.100105","url":null,"abstract":"","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545468","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}
{"title":"Bounds for the augmented Zagreb index","authors":"Qingcuo Ren, Li Wen, Suonan Renqian, Chenxu Yang","doi":"10.20429/tag.2023.10110","DOIUrl":"https://doi.org/10.20429/tag.2023.10110","url":null,"abstract":"","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67546276","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}
{"title":"Ramsey Numbers for Connected 2-Colorings of Complete Graphs","authors":"Mark Budden","doi":"10.20429/tag.2023.10107","DOIUrl":"https://doi.org/10.20429/tag.2023.10107","url":null,"abstract":"","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545526","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 : 2022-10-11DOI: 10.20429/tag.2022.090211
Christian Barrientos
A graceful labeling of a bipartite graph is an α -labeling if it has the property that the labels assigned to the vertices of one stable set of the graph are smaller than the labels assigned to the vertices of the other stable set. A concatenation of cycles is a connected graph formed by a collection of cycles, where each cycle shares at most either two vertices or two edges with other cycles in the collection. In this work we investigate the existence of α -labelings for this kind of graphs, exploring the concepts of vertex amalgamation to produce a family of Eulerian graphs, and edge amalgamation to generate a family of outerplanar graphs. In addition, we determine the number of graphs obtained with k copies of the cycle C n , for both types of amalgamations.
{"title":"Alpha Labeling of Amalgamated Cycles","authors":"Christian Barrientos","doi":"10.20429/tag.2022.090211","DOIUrl":"https://doi.org/10.20429/tag.2022.090211","url":null,"abstract":"A graceful labeling of a bipartite graph is an α -labeling if it has the property that the labels assigned to the vertices of one stable set of the graph are smaller than the labels assigned to the vertices of the other stable set. A concatenation of cycles is a connected graph formed by a collection of cycles, where each cycle shares at most either two vertices or two edges with other cycles in the collection. In this work we investigate the existence of α -labelings for this kind of graphs, exploring the concepts of vertex amalgamation to produce a family of Eulerian graphs, and edge amalgamation to generate a family of outerplanar graphs. In addition, we determine the number of graphs obtained with k copies of the cycle C n , for both types of amalgamations.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42598215","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 : 2022-07-24DOI: 10.20429/tag.2022.090209
K. Haghparast, J. Amjadi, M. Chellali, S. M. Sheikholeslami
{"title":"Restrained reinforcement number in graphs","authors":"K. Haghparast, J. Amjadi, M. Chellali, S. M. Sheikholeslami","doi":"10.20429/tag.2022.090209","DOIUrl":"https://doi.org/10.20429/tag.2022.090209","url":null,"abstract":"","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47975220","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 : 2022-07-24DOI: 10.20429/tag.2022.090208
W. Shiu, R. Low
Let A be a nontrivial abelian group. A connected simple graph G = ( V, E ) is A antimagic if there exists an edge labeling f : E ( G ) → A { 0 } such that the induced vertex labeling f + : V ( G ) → A , defined by f + ( v ) = Σ { f ( u, v ) : ( u, v ) ∈ E ( G ) } , is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs.
{"title":"On the Integer-antimagic Spectra of Non-Hamiltonian Graphs","authors":"W. Shiu, R. Low","doi":"10.20429/tag.2022.090208","DOIUrl":"https://doi.org/10.20429/tag.2022.090208","url":null,"abstract":"Let A be a nontrivial abelian group. A connected simple graph G = ( V, E ) is A antimagic if there exists an edge labeling f : E ( G ) → A { 0 } such that the induced vertex labeling f + : V ( G ) → A , defined by f + ( v ) = Σ { f ( u, v ) : ( u, v ) ∈ E ( G ) } , is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44158484","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 : 2022-07-18DOI: 10.20429/tag.2022.090204
Jared L. Painter, Holleigh C. Landers, Walker Mattox
In [4], it is shown that the disjoint union of an odd cycle and certain paths is harmonious, and that certain starlike trees are harmonious using properties of cosets for a particular subgroup of Z m , where m is the number of edges of the graph. We expand upon these results by first exploring the numerical properties when adding values from cosets and subcosets in Z m . We will then show that these properties may be used to harmoniously label graphs involving a more complex starlike tree, which we will call the snowflake graph.
{"title":"Harmonious Labelings Via Cosets and Subcosets","authors":"Jared L. Painter, Holleigh C. Landers, Walker Mattox","doi":"10.20429/tag.2022.090204","DOIUrl":"https://doi.org/10.20429/tag.2022.090204","url":null,"abstract":"In [4], it is shown that the disjoint union of an odd cycle and certain paths is harmonious, and that certain starlike trees are harmonious using properties of cosets for a particular subgroup of Z m , where m is the number of edges of the graph. We expand upon these results by first exploring the numerical properties when adding values from cosets and subcosets in Z m . We will then show that these properties may be used to harmoniously label graphs involving a more complex starlike tree, which we will call the snowflake graph.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44744771","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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