Domination and Total Domination Contraction Numbers of Graphs
نویسندگان
چکیده
In this paper we consider the effect of edge contraction on the domination number and total domination number of a graph. We define the (total) domination contraction number of a graph as the minimum number of edges that must be contracted in order to decrease the (total) domination number. We show both of this two numbers are at most three for any graph. In view of this result, we classify graphs by their (total) domination contraction numbers and characterize these classes of graphs.
منابع مشابه
Total $k$-Rainbow domination numbers in graphs
Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...
متن کاملDomination and Signed Domination Number of Cayley Graphs
In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.
متن کاملOn independent domination numbers of grid and toroidal grid directed graphs
A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...
متن کاملDomination parameters of Cayley graphs of some groups
In this paper, we investigate domination number, $gamma$, as well as signed domination number, $gamma_{_S}$, of all cubic Cayley graphs of cyclic and quaternion groups. In addition, we show that the domination and signed domination numbers of cubic graphs depend on each other.
متن کاملThe minus k-domination numbers in graphs
For any integer , a minus k-dominating function is afunction f : V (G) {-1,0, 1} satisfying w) for every vertex v, where N(v) ={u V(G) | uv E(G)} and N[v] =N(v)cup {v}. The minimum of the values of v), taken over all minusk-dominating functions f, is called the minus k-dominationnumber and is denoted by $gamma_k^-(G)$ . In this paper, we introduce the study of minu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ars Comb.
دوره 94 شماره
صفحات -
تاریخ انتشار 2010