We investigate polynomial-time approximability of the problems related to edge dominating sets of graphs. When edges are unit-weighted, the edge dominating set problem is polynomially equivalent to the minimum maximal matching problem, in either exact or approximate computation, and the former problem was recently found to be approximable within a factor of 2 even with arbitrary weights. It wil...

It is shown that in star-free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor by any maximal independent set.

Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E′ ⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to de...

Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...

Connected dominating set is widely used in wireless ad-hoc and sensor networks as a routing and topology control backbone to improve the performance and increase the lifetime of the network. Most of the distributed algorithms for approximating connected dominating set are based on constructing maximal independent set. The performance of such algorithms highly depends on the relation between the...

A subset X of edges of a graph G is called an edge dominating set of G if every edge not in X is adjacent to some edge in X . The edge domination number γ′(G) of G is the minimum cardinality taken over all edge dominating sets of G. An edge Roman dominating function of a graph G is a function f : E(G) → {0, 1, 2} such that every edge e with f(e) = 0 is adjacent to some edge e′ with f(e′) = 2. T...

In a graph, vertex dominates itself and its neighbors. A subset S of vertices graph G is double dominating set if every at least twice. The domination number γ ×2 ( ) the minimum cardinality . this paper, we prove that maximal outerplanar order n bounded above by + k /2, where pairs consecutive degree two with distance 3 on outer cycle. We also ×2( ≤ 5 /8 for Hamiltonian planar ≥ 7.

A reduction in temperature lowers the Ca(2+) sensitivity of skinned cardiac myofilaments but this effect is attenuated when native cardiac troponin C (cTnC) is replaced with skeletal TnC. This suggests that conformational differences between the two isoforms mediate the influence of temperature on contractility. To investigate this phenomenon, the functional characteristics of bovine cTnC (BcTn...