For a connected graph G = (V,E) of order at least two, a total restrained monophonic set S of a graph G is a restrained monophonic set S such that the subgraph induced by S has no isolated vertices. The minimum cardinality of a total restrained monophonic set of G is the total restrained monophonic number of G and is denoted by mtr(G). A total restrained monophonic set of cardinality mtr(G) is ...

This paper proposes an MPC - based (model predictive control) scheme to control active and reactive powers of DERs (distributed energy resources) in a grid - connected mode (either through a bus with its associated loads as a PCC (point of common coupling) or an MG (micro - grid)). DER may be a DG (distributed generation) or an ESS (energy storage system). In the proposed scheme, the set - poin...

Introduction. Two nonempty subsets of a topological space are said to be separated if neither intersects the closure of the other. A set is connected if it is not the union of two separated sets. A connected set I is indecomposable if it is not the union of two connected sets, neither of which is dense in I. In [l], Swingle raised the following question: does there exist, in the plane, an indec...

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

The action of a torus group T on a symplectic toric manifold (M, ω) often extends to an effective action of a (nonabelian) compact Lie group G. We may think of T and G as compact Lie subgroups of the symplectomorphism group Symp(M, ω) of (M, ω). On the other hand, (M, ω) is determined by the associated moment polytope P by the result of Delzant [4]. Therefore, the group G should be estimated in...

We consider the problem Maximum Leaf Spanning Tree (MLST) on digraphs, which is defined as follows. Given a digraph G, find a directed spanning tree of G that maximizes the number of leaves. MLST is NP-hard. Existing approximation algorithms for MLST have ratios of O( √ OPT) and 92. We focus on the special case of acyclic digraphs and propose two lineartime approximation algorithms; one with ra...

We develop efficient parameterized, with additive error, approximation algorithms for the (Connected) r-Domination problem and the (Connected) p-Center problem for unweighted and undirected graphs. Given a graph G, we show how to construct a (connected) ( r +O(μ) ) dominating set D with |D| ≤ |D∗| efficiently. Here, D∗ is a minimum (connected) r-dominating set of G and μ is our graph parameter,...