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-...

In this paper, we solve a problem by Glover and Punnen (1997) from the context of domination analysis, where the performance of a heuristic algorithm is rated by the number of solutions that are not better than the solution found by the algorithm, rather than by the relative performance compared to the optimal value. In particular, we show that for the Asymmetric Traveling Salesman Problem (ATS...

Let D be a finite and simple digraph with the vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If∑ x∈N[v] f(x) ≥ 1 for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V (D)) is called the weight w(f) of f . The minimum of weights w(f), taken over all signed dominating function...

Let k ≥ 1 be an integer, and let D = (V, A) be a finite and simple digraph in which dD(v) ≥ k for all v ∈ V . A function f : V −→ {−1, 1} is called a signed total k-dominating function (STkDF) if f(N−(v)) ≥ k for each vertex v ∈ V . The weight w(f) of f is defined by w(f) = ∑ v∈V f(v). The signed total k-domination number for a digraph D is γ kS(D) = min{w(f) | f is a STkDF of D}. In this paper...