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Let ${[n] choose k}$ and ${[n] choose l}$ $( k > l ) $ where $[n] = {1,2,3,...,n}$ denote the family of all $k$-element subsets and $l$-element subsets of $[n]$ respectively. Define a bipartite graph $G_{k,l} = ({[n] choose k},{[n] choose l},E)$ such that two vertices $S, epsilon ,{[n] choose k} $ and $T, epsilon ,{[n] choose l} $ are adjacent if and only if $T subset S$. In this paper, we give an upper bound for the domination number of graph $G_{k,2}$ for $k > lceil frac{n}{2} rceil$ and exact value for $k=n-1$.
Consider all $k$-element subsets and $ell$-element subsets $(k>ell )$ of an $n$-element set as vertices of a bipartite graph. Two vertices are adjacent if the corresponding $ell$-element set is a subset of the corresponding $k$-element set. Let $G_{k
The $k$-power domination problem is a problem in graph theory, which has applications in many areas. However, it is hard to calculate the exact $k$-power domination number since determining k-power domination number of a generic graph is a NP-complet
For a graph $G,$ we consider $D subset V(G)$ to be a porous exponential dominating set if $1le sum_{d in D}$ $left( frac{1}{2} right)^{text{dist}(d,v) -1}$ for every $v in V(G),$ where dist$(d,v)$ denotes the length of the smallest $dv$ path. Similar
The Ramsey number r(K_3,Q_n) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K_N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and ErdH{o}s conjectured
In this paper, we study the domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph. We also compute the domination number of some families of graphs such as star graphs, double start grap