on trees attaining an upper bound on the total domination number

نویسندگان

m. krzywkowski

department of pure and applied mathematics, university of johannesburg, south africa newline research fellow of the claude leon foundation. faculty of electronics, telecommunications and informatics, gdansk university of technology, poland.

چکیده

‎a total dominating set of a graph $g$ is a set $d$ of vertices of $g$ such that every vertex of $g$ has a neighbor in $d$‎. ‎the total domination number of a graph $g$‎, ‎denoted by $gamma_t(g)$‎, ‎is~the minimum cardinality of a total dominating set of $g$‎. ‎chellali and haynes [total and paired-domination numbers of a tree, akce international ournal of graphs and combinatorics 1 (2004)‎, ‎69--75] established the following upper bound on the total domination number of a tree in terms of the order and the number of support vertices‎, ‎$gamma_t(t) le (n+s)/2$‎. ‎we characterize all trees attaining this upper bound‎.‎

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On trees attaining an upper bound on the total domination number

‎A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$‎. ‎The total domination number of a graph $G$‎, ‎denoted by $gamma_t(G)$‎, ‎is~the minimum cardinality of a total dominating set of $G$‎. ‎Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004)‎, ‎6...

متن کامل

On Trees Attaining an Upper Bound on the Total Domination Number

A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γt(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69– 75] established the followin...

متن کامل

An Upper Bound on the First Zagreb Index in Trees

In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.

متن کامل

Upper Bounds on the Total Domination Number

A total dominating set of a graph G with no isolated vertex is a set S of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set in G. In this paper, we present several upper bounds on the total domination number in terms of the minimum degree, diameter, girth and order.

متن کامل

An Upper Bound on F -domination Number in Grids †

A graph G is 2-stratified if its vertex set is colored into two nonempty classes, where one class of vertices colored red and the other color class blue. Let F be a 2-stratified graph rooted at one fixed blue vertex v. The F -domination number of G is the minimum number of red vertices of G in a red-blue coloring of the vertices of G such that for every blue vertex v of G, there is a copy of F ...

متن کامل

An Upper Bound on the Total Outer-independent Domination Number of a Tree

A total outer-independent dominating set of a graph G = (V (G), E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \D is independent. The total outer-independent domination number of a graph G, denoted by γ t (G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n ≥ 4, with l le...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید


عنوان ژورنال:
bulletin of the iranian mathematical society

جلد ۴۱، شماره ۶، صفحات ۱۳۳۹-۱۳۴۴

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023