

A New Notion of Energy of Digraphs





نویسنده

Khan Mehtab

منبع

Iranian Journal Of Mathematical Chemistry  2021  دوره : 12  شماره : 2  صفحه:111 125



چکیده

The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. let z1(. . . zn be the eigenvalues of an nvertex digraph d. here, we give a new notion of energy of digraphs defined by ep (d ) =∑^n k = 1 r (zk) 3 (zk)  , where r (zk) and s (zk) are real and imaginary parts of zk, respectively. we call it ppenergy of the digraph and compute the penergy formulas for directed cycles. for n > 1 2 , it is shown that ppenergy of directed cycles increases monotonically with respect to their order. the unicyclic digraphs with smallest and largest penergy are obtained and counter examples will be presented to show that the penergy of a digraph does not possess increasingproperty with respect to quasiorder relation over the set , where is the set of nvertex digraphs with cycles of length . also, an upper bound for the penergy is presented and give all digraphs which attain this bound.

کلیدواژه

Energy ,Iota Energy ,Digraphs ,PEnergy

آدرس

Anhui University, School Of Mathematical Sciences, China

پست الکترونیکی

mehtabkhan85@gmail.com












Authors















