Pub Date : 2022-08-12DOI: 10.1007/s00373-022-02536-5
Ting-Fang Li, H. Ren
{"title":"The Number of Copies of K2, t+1 in a Graph","authors":"Ting-Fang Li, H. Ren","doi":"10.1007/s00373-022-02536-5","DOIUrl":"https://doi.org/10.1007/s00373-022-02536-5","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79878823","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 : 2022-08-09DOI: 10.1007/s00373-022-02531-w
Gang Chen, Z. Miao, Zi-Xia Song, Jingmei Zhang
{"title":"On the Size of (Kt, Pk)-Co-Critical Graphs","authors":"Gang Chen, Z. Miao, Zi-Xia Song, Jingmei Zhang","doi":"10.1007/s00373-022-02531-w","DOIUrl":"https://doi.org/10.1007/s00373-022-02531-w","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89746642","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 : 2022-07-22DOI: 10.1007/s00373-022-02517-8
Tala Abuadas, C. Hoàng
{"title":"On the Structure of Graphs Without Claw, 4K1 and co-R","authors":"Tala Abuadas, C. Hoàng","doi":"10.1007/s00373-022-02517-8","DOIUrl":"https://doi.org/10.1007/s00373-022-02517-8","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83354428","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 : 2022-07-15DOI: 10.1080/09728600.2022.2094736
Priyamvada, B. S. Panda
{"title":"Exact square coloring of graphs resulting from some graph operations and products","authors":"Priyamvada, B. S. Panda","doi":"10.1080/09728600.2022.2094736","DOIUrl":"https://doi.org/10.1080/09728600.2022.2094736","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82754096","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 : 2022-07-12DOI: 10.1080/09728600.2022.2094735
Fatemeh Nahani Pour, H. A. Ahangar, M. Chellali, S. M. Sheikholeslami
{"title":"An improved upper bound on the independent double Roman domination number of trees","authors":"Fatemeh Nahani Pour, H. A. Ahangar, M. Chellali, S. M. Sheikholeslami","doi":"10.1080/09728600.2022.2094735","DOIUrl":"https://doi.org/10.1080/09728600.2022.2094735","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78444186","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 : 2022-07-08DOI: 10.1080/09728600.2023.2250837
Hortensia Galeana-S'anchez, Carlos Vilchis-Alfaro
Alternating Euler trails has been extensively studied for its diverse applications, for example, in genetic and molecular biology, social science and channel assignment in wireless networks, as well as for theoretical reasons. We will consider the following edge-coloring. Let $H$ be a graph possibly with loops and $G$ a graph without loops. An $H$-coloring of $G$ is a function $c: E(G) rightarrow V(H)$. We will say that $G$ is an $H$-colored graph whenever we are taking a fixed $H$-coloring of $G$. A sequence $W=(v_0,e_0^1, ldots, e_0^{k_0},v_1,e_1^1,ldots,e_{n-1}^{k_{n-1}},v_n)$ in $G$, where for each $i in {0,ldots, n-1}$, $k_i geq 1$ and $e_i^j = v_iv_{i+1}$ is an edge in $G$, for every $j in {1,ldots, k_i }$, is a dynamic $H$-trail if $W$ does not repeat edges and $c(e_i^{k_i})c(e_{i+1}^1)$ is an edge in $H$, for each $i in {0,ldots,n-2}$. In particular a dynamic $H$-trail is an alternating Euler trail when $H$ is a complete graph without loops and $k_i=1$, for every $i in {1,ldots,n-1}$. In this paper, we introduce the concept of dynamic $H$-trail, which arises in a natural way in the modeling of many practical problems, in particular, in theoretical computer science. We provide necessary and sufficient conditions for the existence of closed Euler dynamic $H$-trail in $H$-colored multigraphs. Also we provide polynomial time algorithms that allows us to convert a cycle in an auxiliary graph, $L_2^H(G)$, in a closed dynamic H-trail in $G$, and vice versa, where $L_2^H(G)$ is a non-colored simple graph obtained from $G$ in a polynomial time.
{"title":"Euler dynamic H-trails in edge-colored graphs","authors":"Hortensia Galeana-S'anchez, Carlos Vilchis-Alfaro","doi":"10.1080/09728600.2023.2250837","DOIUrl":"https://doi.org/10.1080/09728600.2023.2250837","url":null,"abstract":"Alternating Euler trails has been extensively studied for its diverse applications, for example, in genetic and molecular biology, social science and channel assignment in wireless networks, as well as for theoretical reasons. We will consider the following edge-coloring. Let $H$ be a graph possibly with loops and $G$ a graph without loops. An $H$-coloring of $G$ is a function $c: E(G) rightarrow V(H)$. We will say that $G$ is an $H$-colored graph whenever we are taking a fixed $H$-coloring of $G$. A sequence $W=(v_0,e_0^1, ldots, e_0^{k_0},v_1,e_1^1,ldots,e_{n-1}^{k_{n-1}},v_n)$ in $G$, where for each $i in {0,ldots, n-1}$, $k_i geq 1$ and $e_i^j = v_iv_{i+1}$ is an edge in $G$, for every $j in {1,ldots, k_i }$, is a dynamic $H$-trail if $W$ does not repeat edges and $c(e_i^{k_i})c(e_{i+1}^1)$ is an edge in $H$, for each $i in {0,ldots,n-2}$. In particular a dynamic $H$-trail is an alternating Euler trail when $H$ is a complete graph without loops and $k_i=1$, for every $i in {1,ldots,n-1}$. In this paper, we introduce the concept of dynamic $H$-trail, which arises in a natural way in the modeling of many practical problems, in particular, in theoretical computer science. We provide necessary and sufficient conditions for the existence of closed Euler dynamic $H$-trail in $H$-colored multigraphs. Also we provide polynomial time algorithms that allows us to convert a cycle in an auxiliary graph, $L_2^H(G)$, in a closed dynamic H-trail in $G$, and vice versa, where $L_2^H(G)$ is a non-colored simple graph obtained from $G$ in a polynomial time.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43321208","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 : 2022-07-06DOI: 10.1080/09728600.2022.2094734
Deepti Jain, Purnima Gupta
{"title":"Independent 2-point set domination in graphs - II","authors":"Deepti Jain, Purnima Gupta","doi":"10.1080/09728600.2022.2094734","DOIUrl":"https://doi.org/10.1080/09728600.2022.2094734","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86879174","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 : 2022-07-06DOI: 10.1080/09728600.2022.2093146
Jay S. Bagga, L. Beineke
{"title":"New results and open problems in line graphs","authors":"Jay S. Bagga, L. Beineke","doi":"10.1080/09728600.2022.2093146","DOIUrl":"https://doi.org/10.1080/09728600.2022.2093146","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84608096","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 : 2022-07-06DOI: 10.1080/09728600.2022.2093686
A. Jahanbani, S. M. Sheikholeslami
{"title":"The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs","authors":"A. Jahanbani, S. M. Sheikholeslami","doi":"10.1080/09728600.2022.2093686","DOIUrl":"https://doi.org/10.1080/09728600.2022.2093686","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88860321","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 : 2022-07-04DOI: 10.1080/09728600.2022.2093145
Jishnu Sen, S. Kola
{"title":"Broadcast domination of lexicographic and modular products of graphs","authors":"Jishnu Sen, S. Kola","doi":"10.1080/09728600.2022.2093145","DOIUrl":"https://doi.org/10.1080/09728600.2022.2093145","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90224604","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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