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ON THE NEW EXTENSION OF DISTANCE-BALANCED GRAPHS 关于距离平衡图的新推广
IF 0.4
Transactions on Combinatorics Pub Date : 2016-12-01 DOI: 10.22108/TOC.2016.15048
M. Faghani, E. Pourhadi, H. Kharazi
{"title":"ON THE NEW EXTENSION OF DISTANCE-BALANCED GRAPHS","authors":"M. Faghani, E. Pourhadi, H. Kharazi","doi":"10.22108/TOC.2016.15048","DOIUrl":"https://doi.org/10.22108/TOC.2016.15048","url":null,"abstract":"‎In this paper‎, ‎we initially introduce the concept of $n$-distance-balanced property which is considered as the generalized concept of distance-balanced property‎. ‎In our consideration‎, ‎we also define the new concept locally regularity in order to find a connection between $n$-distance-balanced graphs and their lexicographic product‎. ‎Furthermore‎, ‎we include a characteristic method which is practicable and can be used to classify all graphs with $i$-distance-balanced properties for $ i=2,3 $ which is also relevant to the concept of total distance‎. ‎Moreover‎, ‎we conclude a connection between distance-balanced and 2-distance-balanced graphs‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"21-34"},"PeriodicalIF":0.4,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208507","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: 5
Extremal tetracyclic graphs with respect to the first and second Zagreb indices 关于第一和第二萨格勒布指数的极值四环图
IF 0.4
Transactions on Combinatorics Pub Date : 2016-12-01 DOI: 10.22108/TOC.2016.12878
N. Habibi, Tayebeh Dehghan Zadeh, A. Ashrafi
{"title":"Extremal tetracyclic graphs with respect to the first and second Zagreb indices","authors":"N. Habibi, Tayebeh Dehghan Zadeh, A. Ashrafi","doi":"10.22108/TOC.2016.12878","DOIUrl":"https://doi.org/10.22108/TOC.2016.12878","url":null,"abstract":"‎The first Zagreb index‎, ‎$M_1(G)$‎, ‎and second Zagreb index‎, ‎$M_2(G)$‎, ‎of the graph $G$ is defined as $M_{1}(G)=sum_{vin‎ ‎V(G)}d^{2}(v)$ and $M_{2}(G)=sum_{e=uvin E(G)}d(u)d(v),$ where‎ ‎$d(u)$ denotes the degree of vertex $u$‎. ‎In this paper‎, ‎the first‎ ‎and second maximum values of the first and second Zagreb indices‎ ‎in the class of all $n-$vertex tetracyclic graphs are presented‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"35-55"},"PeriodicalIF":0.4,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208359","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
Some results on the comaximal ideal graph of a commutative ring 交换环的极大理想图的一些结果
IF 0.4
Transactions on Combinatorics Pub Date : 2016-12-01 DOI: 10.22108/TOC.2016.15047
H. Dorbidi, R. Manaviyat
{"title":"Some results on the comaximal ideal graph of a commutative ring","authors":"H. Dorbidi, R. Manaviyat","doi":"10.22108/TOC.2016.15047","DOIUrl":"https://doi.org/10.22108/TOC.2016.15047","url":null,"abstract":"Let $R$ be a commutative ring with unity. The comaximal ideal graph of $R$, denoted by $mathcal{C}(R)$, is a graph whose vertices are the proper ideals of $R$ which are not contained in the Jacobson radical of $R$, and two vertices $I_1$ and $I_2$ are adjacent if and only if $I_1 +I_2 = R$. In this paper, we classify all comaximal ideal graphs with finite independence number and present a formula to calculate this number. Also, the domination number of $mathcal{C}(R)$ for a ring $R$ is determined. In the last section, we introduce all planar and toroidal comaximal ideal graphs. Moreover, the commutative rings with isomorphic comaximal ideal graphs are characterized. In particular we show that every finite comaximal ideal graph is isomorphic to some $mathcal{C}(mathbb{Z}_n)$.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"9-20"},"PeriodicalIF":0.4,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208332","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: 4
New class of integral bipartite graphs with large diameter 一类新的大直径积分二部图
IF 0.4
Transactions on Combinatorics Pub Date : 2016-11-23 DOI: 10.22108/toc.2016.20738
A. F. Laali, H. Javadi
{"title":"New class of integral bipartite graphs with large diameter","authors":"A. F. Laali, H. Javadi","doi":"10.22108/toc.2016.20738","DOIUrl":"https://doi.org/10.22108/toc.2016.20738","url":null,"abstract":". In this paper, we construct a new class of integral bipartite graphs (not necessarily trees) with large even diameters. In fact, for every finite set A of positive integers of size k we construct an integral bipartite graph G of diameter 2 k such that the set of positive eigenvalues of G is exactly A . This class of integral bipartite graphs has never found before.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"13-17"},"PeriodicalIF":0.4,"publicationDate":"2016-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208571","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
Extreme edge-friendly indices of complete bipartite graphs 完全二部图的极边友好指标
IF 0.4
Transactions on Combinatorics Pub Date : 2016-09-01 DOI: 10.22108/TOC.2016.12473
W. Shiu
{"title":"Extreme edge-friendly indices of complete bipartite graphs","authors":"W. Shiu","doi":"10.22108/TOC.2016.12473","DOIUrl":"https://doi.org/10.22108/TOC.2016.12473","url":null,"abstract":"Let $G=(V,E)$ be a simple graph‎. ‎An edge labeling $f:Eto {0,1}$ induces a vertex labeling $f^+:Vto Z_2$ defined by $f^+(v)equiv sumlimits_{uvin E} f(uv)pmod{2}$ for each $v in V$‎, ‎where $Z_2={0,1}$ is the additive group of order 2‎. ‎For $iin{0,1}$‎, ‎let‎ ‎$e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$‎. ‎A labeling $f$ is called edge-friendly if‎ ‎$|e_f(1)-e_f(0)|le 1$‎. ‎$I_f(G)=v_f(1)-v_f(0)$ is called the edge-friendly index of $G$ under an edge-friendly labeling $f$‎. ‎Extreme values of edge-friendly index of complete bipartite graphs will be determined‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"11-21"},"PeriodicalIF":0.4,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208281","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: 2
A NEW CONSTRUCTION FOR VERTEX DECOMPOSABLE GRAPHS 顶点可分解图的一种新构造
IF 0.4
Transactions on Combinatorics Pub Date : 2016-09-01 DOI: 10.22108/TOC.2016.13316
N. Hajisharifi, A. Tehranian
{"title":"A NEW CONSTRUCTION FOR VERTEX DECOMPOSABLE GRAPHS","authors":"N. Hajisharifi, A. Tehranian","doi":"10.22108/TOC.2016.13316","DOIUrl":"https://doi.org/10.22108/TOC.2016.13316","url":null,"abstract":"Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x in V(G)$. The graph $Gcup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $Gsetminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G cup W(S)$ is a vertex decomposable graph.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"33-38"},"PeriodicalIF":0.4,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208402","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
Steiner Wiener index of graph products 图积的Steiner Wiener指数
IF 0.4
Transactions on Combinatorics Pub Date : 2016-09-01 DOI: 10.22108/TOC.2016.13499
Yaoping Mao, Zhao Wang, I. Gutman
{"title":"Steiner Wiener index of graph products","authors":"Yaoping Mao, Zhao Wang, I. Gutman","doi":"10.22108/TOC.2016.13499","DOIUrl":"https://doi.org/10.22108/TOC.2016.13499","url":null,"abstract":"The Wiener index $W(G)$ of a connected graph $G$‎ ‎is defined as $W(G)=sum_{u,vin V(G)}d_G(u,v)$‎ ‎where $d_G(u,v)$ is the distance between the vertices $u$ and $v$ of‎ ‎$G$‎. ‎For $Ssubseteq V(G)$‎, ‎the Steiner distance $d(S)$ of‎ ‎the vertices of $S$ is the minimum size of a connected subgraph of‎ ‎$G$ whose vertex set is $S$‎. ‎The  $k$-th Steiner Wiener index‎ ‎$SW_k(G)$ of $G$ is defined as‎ ‎$SW_k(G)=sum_{overset{Ssubseteq V(G)}{|S|=k}} d(S)$‎. ‎We establish‎ ‎expressions for the $k$-th Steiner Wiener index on the join‎, ‎corona‎, ‎cluster‎, ‎lexicographical product‎, ‎and Cartesian product of graphs‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"39-50"},"PeriodicalIF":0.4,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208453","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: 22
A new $O(m+k n log overline{d})$ algorithm to find the $k$ shortest paths in acyclic digraphs 一种新的$O(m+k n log overline{d})$算法，用于在无环有向图中找到$k$最短路径
IF 0.4
Transactions on Combinatorics Pub Date : 2016-09-01 DOI: 10.22108/TOC.2016.12602
M. Kadivar
{"title":"A new $O(m+k n log overline{d})$ algorithm to find the $k$ shortest paths in acyclic digraphs","authors":"M. Kadivar","doi":"10.22108/TOC.2016.12602","DOIUrl":"https://doi.org/10.22108/TOC.2016.12602","url":null,"abstract":"‎We give an algorithm‎, ‎called T$^{*}$‎, ‎for finding the k shortest simple paths connecting a certain‎ ‎pair of nodes‎, ‎$s$ and $t$‎, ‎in a acyclic digraph‎. ‎First the nodes of the graph are labeled according to the topological ordering‎. ‎Then for node $i$ an ordered list of simple $s-i$ paths is created‎. ‎The length of the list is at most $k$ and it is created by using tournament trees‎. ‎We prove the correctness of T$^{*}$ and show that its worst-case complexity is $O(m+k n log overline{d})$ in which n is the number of nodes and m is the number of arcs and $overline{d}$ is the mean degree of the graph‎. ‎The algorithm has a space complexity of $O(kn)$ which entails an important improvement in space complexity‎. ‎An experimental evaluation of T$^{*}$ is presented which confirms the advantage of our algorithm compared to the‎ ‎most efficient $k$ shortest paths algorithms known so far‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"64 1","pages":"23-31"},"PeriodicalIF":0.4,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208341","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
Total $k$-distance domination critical graphs 总$k$距离支配临界图
IF 0.4
Transactions on Combinatorics Pub Date : 2016-09-01 DOI: 10.22108/TOC.2016.11972
D. Mojdeh, A. Sayed-Khalkhali, H. A. Ahangar, Yancai Zhao
{"title":"Total $k$-distance domination critical graphs","authors":"D. Mojdeh, A. Sayed-Khalkhali, H. A. Ahangar, Yancai Zhao","doi":"10.22108/TOC.2016.11972","DOIUrl":"https://doi.org/10.22108/TOC.2016.11972","url":null,"abstract":"A set $S$ of vertices in a graph $G=(V,E)$ is called a total‎ ‎$k$-distance dominating set if every vertex in $V$ is within‎ ‎distance $k$ of a vertex in $S$‎. ‎A graph $G$ is total $k$-distance‎ ‎domination-critical if $gamma_{t}^{k} (G‎ - ‎x) < gamma_{t}^{k}‎ ‎(G)$ for any vertex $xin V(G)$‎. ‎In this paper‎, ‎we investigate some results on total $k$-distance domination-critical of graphs‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"1-9"},"PeriodicalIF":0.4,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208265","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: 5
DEGREE DISTANCE AND GUTMAN INDEX OF INCREASING TREES 增殖树度、距离和古特曼指数
IF 0.4
Transactions on Combinatorics Pub Date : 2016-06-01 DOI: 10.22108/TOC.2016.9915
R. Kazemi, Leila Khaleghi Meimondari
{"title":"DEGREE DISTANCE AND GUTMAN INDEX OF INCREASING TREES","authors":"R. Kazemi, Leila Khaleghi Meimondari","doi":"10.22108/TOC.2016.9915","DOIUrl":"https://doi.org/10.22108/TOC.2016.9915","url":null,"abstract":"‎‎The Gutman index and degree distance of a connected graph $G$ are defined as‎ ‎begin{eqnarray*}‎ ‎textrm{Gut}(G)=sum_{{u,v}subseteq V(G)}d(u)d(v)d_G(u,v)‎, ‎end{eqnarray*}‎ ‎and‎ ‎begin{eqnarray*}‎ ‎DD(G)=sum_{{u,v}subseteq V(G)}(d(u)+d(v))d_G(u,v)‎, ‎end{eqnarray*}‎ ‎respectively‎, ‎where‎ ‎$d(u)$ is the degree of vertex $u$ and $d_G(u,v)$ is the distance between vertices $u$ and $v$‎. ‎In this paper‎, ‎through a recurrence equation for the Wiener index‎, ‎we study the first two‎ ‎moments of the Gutman index and degree distance of increasing‎ ‎trees‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"23-31"},"PeriodicalIF":0.4,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68209063","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: 3
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