Pub Date : 2023-12-18DOI: 10.1080/09728600.2023.2291465
M. Korivand, K. Khashyarmanesh, M. Tavakoli
{"title":"Mixed metric dimension over (edge) corona products","authors":"M. Korivand, K. Khashyarmanesh, M. Tavakoli","doi":"10.1080/09728600.2023.2291465","DOIUrl":"https://doi.org/10.1080/09728600.2023.2291465","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139173575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-14DOI: 10.1080/09728600.2023.2282105
Jeny Jacob, M. Changat
{"title":"First-order logic with metric betweenness – the case of non-definability of some graph classes","authors":"Jeny Jacob, M. Changat","doi":"10.1080/09728600.2023.2282105","DOIUrl":"https://doi.org/10.1080/09728600.2023.2282105","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138974042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-14DOI: 10.1080/09728600.2023.2290036
Peter J. Cameron
{"title":"What can graphs and algebraic structures say to each other?","authors":"Peter J. Cameron","doi":"10.1080/09728600.2023.2290036","DOIUrl":"https://doi.org/10.1080/09728600.2023.2290036","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138975022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-07DOI: 10.1080/09728600.2023.2280799
S. Prabhu, D. Sagaya Rani Jeba, M. Arulperumjothi, Sandi Klavžar
{"title":"Metric Dimension of Irregular Convex Triangular Networks","authors":"S. Prabhu, D. Sagaya Rani Jeba, M. Arulperumjothi, Sandi Klavžar","doi":"10.1080/09728600.2023.2280799","DOIUrl":"https://doi.org/10.1080/09728600.2023.2280799","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138591515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let G=(V,E) be a graph of order n and let f:V→{1,2…,n} be a bijection. For every vertex v∈V, we define the weight of the vertex v as w(v)=∑x∈N(v)f(x) where N(v) is the open neighborhood of the vertex v. The bijection f is said to be a local distance antimagic labeling of G if w(u)≠w(v) for every pair of adjacent vertices u,v∈V. The local distance antimagic labeling f defines a proper vertex coloring of the graph G, where the vertex v is assigned the color w(v). We define the local distance antimagic chromatic number χld(G) to be the minimum number of colors taken over all colorings induced by local distance antimagic labelings of G. In this paper we obtain the local distance antimagic labelings for several families of graphs including the path Pn, the cycle Cn, the wheel graph Wn, friendship graph Fn, the corona product of graphs G°Km¯, complete multipartite graph and some special types of the caterpillars. We also find upper bounds for the local distance antimagic chromatic number for these families of graphs.
{"title":"On local distance antimagic labeling of graphs","authors":"Adarsh Kumar Handa, Aloysius Godinho, Tarkeshwar Singh","doi":"10.1080/09728600.2023.2256811","DOIUrl":"https://doi.org/10.1080/09728600.2023.2256811","url":null,"abstract":"Let G=(V,E) be a graph of order n and let f:V→{1,2…,n} be a bijection. For every vertex v∈V, we define the weight of the vertex v as w(v)=∑x∈N(v)f(x) where N(v) is the open neighborhood of the vertex v. The bijection f is said to be a local distance antimagic labeling of G if w(u)≠w(v) for every pair of adjacent vertices u,v∈V. The local distance antimagic labeling f defines a proper vertex coloring of the graph G, where the vertex v is assigned the color w(v). We define the local distance antimagic chromatic number χld(G) to be the minimum number of colors taken over all colorings induced by local distance antimagic labelings of G. In this paper we obtain the local distance antimagic labelings for several families of graphs including the path Pn, the cycle Cn, the wheel graph Wn, friendship graph Fn, the corona product of graphs G°Km¯, complete multipartite graph and some special types of the caterpillars. We also find upper bounds for the local distance antimagic chromatic number for these families of graphs.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136023243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-14DOI: 10.1080/09728600.2023.2265994
Kusum S. Rajbhar, Rajendra M. Pawale
The block graph of a quasi-symmetric design is strongly regular. It is a challenging problem to decide which strongly regular graphs are block graphs of quasi-symmetric designs. We rule out the possibility of quasi-symmetric designs with non-zero intersection numbers whose block graphs have the parameters as certain pseudo-geometric graphs.
{"title":"Non-existence of quasi-symmetric designs having certain pseudo-geometric block graphs","authors":"Kusum S. Rajbhar, Rajendra M. Pawale","doi":"10.1080/09728600.2023.2265994","DOIUrl":"https://doi.org/10.1080/09728600.2023.2265994","url":null,"abstract":"The block graph of a quasi-symmetric design is strongly regular. It is a challenging problem to decide which strongly regular graphs are block graphs of quasi-symmetric designs. We rule out the possibility of quasi-symmetric designs with non-zero intersection numbers whose block graphs have the parameters as certain pseudo-geometric graphs.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135803190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1080/09728600.2023.2263039
Yueping Su, Lieying Liao, Shaoqiang Liu
Topological indices play an important role in mathematical chemistry, particularly in studies of quantitative structure property and quantitative structure activity relationships. The eccentric harmonic index of G is defined as He(G)=∑uv∈E(G)2e(u)+e(v), where uv is an edge of G, e(u) is the eccentricity of the vertex u in G. In this paper, we will determine the maximum and minmum eccentric harmonic index of trees in terms of graph parameters such as pendant number and matching number, and characterize corresponding extremal graphs.
{"title":"The eccentric harmonic index of trees","authors":"Yueping Su, Lieying Liao, Shaoqiang Liu","doi":"10.1080/09728600.2023.2263039","DOIUrl":"https://doi.org/10.1080/09728600.2023.2263039","url":null,"abstract":"Topological indices play an important role in mathematical chemistry, particularly in studies of quantitative structure property and quantitative structure activity relationships. The eccentric harmonic index of G is defined as He(G)=∑uv∈E(G)2e(u)+e(v), where uv is an edge of G, e(u) is the eccentricity of the vertex u in G. In this paper, we will determine the maximum and minmum eccentric harmonic index of trees in terms of graph parameters such as pendant number and matching number, and characterize corresponding extremal graphs.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1080/09728600.2023.2263040
Balamoorthy S., Kavaskar T., Vinothkumar K
The Wiener index of a connected graph G is W(G)=∑{u,v}⊆V(G)dG(u,v). In this paper, we obtain the Wiener index of H-generalized join of graphs G1,G2,…,Gk. As a consequence, we obtain some earlier known results in [Alaeiyan et al. in Aust. J. Basic Appl. Sci. (2011) 5(12): 145–152; Yeh et al. in Discrete Math. (1994) 135: 359–365] and we also obtain the Wiener index of the generalized corona product of graphs. We further show that the ideal-based zero-divisor graph ΓI(R) is a H-generalized join of complete graphs and totally disconnected graphs. As a result, we find the Wiener index of the ideal-based zero-divisor graph ΓI(R) and we deduce some of the main results in [Selvakumar et al. in Discrete Appl. Math. (2022) 311: 72–84]. Moreover, we show that W(ΓI(Zn)) is a quadratic polynomial in n, where Zn is the ring of integers modulo n and we calculate the exact value of the Wiener index of ΓNil(R)(R), where Nil(R) is nilradical of R. Furthermore, we give a Python program for computing the Wiener index of ΓI(Zn) if I is an ideal of Zn generated by pr, where pr is a proper divisor of n, p is a prime number and r is a positive integer with r≥2.
{"title":"Wiener index of an ideal-based zero-divisor graph of commutative ring with unity","authors":"Balamoorthy S., Kavaskar T., Vinothkumar K","doi":"10.1080/09728600.2023.2263040","DOIUrl":"https://doi.org/10.1080/09728600.2023.2263040","url":null,"abstract":"The Wiener index of a connected graph G is W(G)=∑{u,v}⊆V(G)dG(u,v). In this paper, we obtain the Wiener index of H-generalized join of graphs G1,G2,…,Gk. As a consequence, we obtain some earlier known results in [Alaeiyan et al. in Aust. J. Basic Appl. Sci. (2011) 5(12): 145–152; Yeh et al. in Discrete Math. (1994) 135: 359–365] and we also obtain the Wiener index of the generalized corona product of graphs. We further show that the ideal-based zero-divisor graph ΓI(R) is a H-generalized join of complete graphs and totally disconnected graphs. As a result, we find the Wiener index of the ideal-based zero-divisor graph ΓI(R) and we deduce some of the main results in [Selvakumar et al. in Discrete Appl. Math. (2022) 311: 72–84]. Moreover, we show that W(ΓI(Zn)) is a quadratic polynomial in n, where Zn is the ring of integers modulo n and we calculate the exact value of the Wiener index of ΓNil(R)(R), where Nil(R) is nilradical of R. Furthermore, we give a Python program for computing the Wiener index of ΓI(Zn) if I is an ideal of Zn generated by pr, where pr is a proper divisor of n, p is a prime number and r is a positive integer with r≥2.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.1080/09728600.2023.2254562
Gary Chartrand, Ebrahim Salehi, Ping Zhang
{"title":"On subset labelings of trees","authors":"Gary Chartrand, Ebrahim Salehi, Ping Zhang","doi":"10.1080/09728600.2023.2254562","DOIUrl":"https://doi.org/10.1080/09728600.2023.2254562","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135879715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-04DOI: 10.1080/09728600.2023.2250407
Y. Egawa, Keiko Kotani, Jumpei Yamamoto
{"title":"Existence of 4-factors in star-free graphs with edge-connectivity conditions","authors":"Y. Egawa, Keiko Kotani, Jumpei Yamamoto","doi":"10.1080/09728600.2023.2250407","DOIUrl":"https://doi.org/10.1080/09728600.2023.2250407","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44475625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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