Ordering of bicyclic signed digraphs by energy

Let Sn be the class of bicyclic signed digraphs with n vertices whose two signed directed even cycles are vertex-disjoint. In this paper, we characterize the ordering of bicyclic signed digraphs in Sn by energy with two positive or negative directed even cycles (resp., one positive directed even cycle and one negative directed even cycle). Furthermore, we determine extremal energy in Sn by the two orderings.

Iota energy of bicyclic signed digraphs

Iota energy of signed digraphs is defined as sum of absolute values of imaginary parts of its eigenvalues. Extremal energy and iota energy of unicyclic signed digraphs is known. In this paper, we address the problem of finding signed digraphs with extremal iota energy among vertex-disjoint bicyclic signed digraphs of fixed order.

Computing extremal energy of a class of bicyclic weighted digraphs

The energy of a weighted digraph [Formula: see text] is the sum of absolute values of real part of its eigenvalues. Recently, the minimal and maximal energy of unicyclic weighted digraphs with cycle weight [Formula: see text] is studied. In this paper, we introduce a class [Formula: see text] of those bicyclic weighted digraphs of fixed order which contain vertex-disjoint weighted cycles of weights [Formula: see text] or [Formula: see text] and [Formula: see text] or [Formula: see text], where [Formula: see text]. We find digraphs in [Formula: see text] under certain conditions on [Formula: see text] and [Formula: see text] with extremal energy.