We study the complexity of two dual covering and packing distance-based problems Broadcast Domination Multipacking in digraphs. A dominating broadcast a digraph D is function $$f:V(D)\rightarrow {\mathbb {N}}$$ such that for each vertex v D, there exists t with $$f(t)>0$$ having directed path to length at most f(t). The cost f sum f(v) over all vertices v. multipacking set S every integer d, ar...

We show in this paper that the upper minus domination number −(G) of a claw-free cubic graph G is at most 1 2 |V (G)|. © 2006 Published by Elsevier B.V.

Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this  paper, we give some new methods to construct new skew-equienergetic digraphs.

Dual digraphs of finite join-semidistributive lattices, meet-semidistributive lattices and semidistributive are characterised. The vertices the dual maximal disjoint filter-ideal pairs lattice. approach used here combines representations arbitrary due to Urquhart (1978) Ploščica (1995). duals mainly viewed as TiRS they were presented studied in Craig--Gouveia--Haviar (2015 2022). When appropria...

The domination graph of a digraph has the same vertices as the digraph with an edge between two vertices if every other vertex loses to at least one of the two. Previously, the authors showed that the domination graph of a tournament is either an odd cycle with or without isolated and/or pendant vertices, or a forest of caterpillars. They also showed that any graph consisting of an odd cycle wi...

The Generalized Traveling Salesman Problem (GTSP) is stated as follows. Given a weighted complete digraph K∗ n and a partition V1, . . . , Vk of its vertices, find a minimum weight cycle containing exactly one vertex from each set Vi, i = 1, . . . , k. We study transformations from GTSP to TSP. The ’exact’ Noon-Bean transformation is investigated in computational experiments. We study the ’non-...