Given a graph $$G=(V,E)$$ and an integer k, the Minimum Membership Dominating Set (MMDS) problem seeks to find dominating set $$S \subseteq V$$ of G such that for each $$v \in , $$\vert N[v] \cap S\vert $$ is at most k. We investigate parameterized complexity obtain following results MMDS problem. First, we show NP-hard even on planar bipartite graphs. Next, W[1]-hard parameter pathwidth (and t...

abstract. let $l$ be a lattice with the least element $0$. an element $xin l$ is a zero divisor if $xwedge y=0$ for some $yin l^*=lsetminus left{0right}$. the set of all zero divisors is denoted by $z(l)$. we associate a simple graph $gamma(l)$ to $l$ with vertex set $z(l)^*=z(l)setminus left{0right}$, the set of non-zero zero divisors of $l$ and distinct $x,yin z(l)^*$ are adjacent if and only...

In the token jumping problem for a vertex subset problem Q on graphs we are given a graph G and two feasible solutions Ss, St ⊆ V (G) of Q with |Ss| = |St|, and imagine that a token is placed on each vertex of Ss. The problem is to determine whether there exists a sequence S1, . . . , Sn of feasible solutions, where S1 = Ss, Sn = St and each Si+1 results from Si, 1 ≤ i < n, by moving exactly on...