In [2] (and earlier in [3]), we defined several global communication tasks (universal exchange, universal broadcast, universal summation) on directed or vertex symmetric networks. In that paper, we mainly focused on universal broadcast. In [4], we discussed universal sum. Here we continue this work and focus on universal exchange (transpose) in directed vertex symmetric graphs. Introduction. In...

An even factor in a digraph, introduced by Cunningham and Geelen (2001), is a collection of vertex-disjoint dipaths and even dicycles, which generalizes a path-matching of Cunningham and Geelen (1997). In a restricted class of digraphs, called odd-cyclesymmetric, Pap (2005) presented a combinatorial algorithm to find a maximum even factor. For odd-cycle-symmetric weighted digraphs, which are od...

Chordal graphs are important in the structural and algorithmic graph theory. A digraph analogue of chordal was introduced by Haskin Rose 1973 but has not been subject active studies until recently when a characterization semicomplete digraphs terms forbidden subdigraphs found Meister Telle. Locally digraphs, quasi-transitive extended amongst most popular generalizations digraphs. We extend subd...

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.

The exponent of a primitive digraph is the smallest integer k such that for each ordered pair of (not necessarily distinct) vertices x and y there is a walk of length k from x to y. As a generalization of exponent, Brualdi and Liu (Linear Algebra Appl. 14 (1990) 483499) introduced three types of generalized exponents for primitive digraphs in 1990. In this Paper we extend their definitions of g...

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...