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We study the General Routing Problem defined on a mixed graph and with stochastic demands.

Let M be a mixed graph and (H(M)) be its Hermitian-adjacency matrix.

We propose to study sandwich problems for properties Π concerning orientations, such as Eulerian orientation of a mixed graph and orientation with given in-degrees of a graph.

If M is a mixed graph and its underlying graph (M_{U}) is r regular, then (R_{-1}(M_{U} =frac{m}{r^{2}}) and (2m=nr).

Let M be a mixed graph and its underlying graph (M_{U}) be r (≠0) regular and (E(M_{U} =m).

In this paper we propose to study sandwich problems for properties Π concerning orientations, such as Eulerian orientation of a mixed graph and orientation with given in-degrees of a graph, or more generally of a mixed graph.

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Silverbush et al. [ 9] recently formulated a polynomial-size integer linear program for the generalization of mixed graphs and did some experiments with it.

In this paper, we define the Hermitian-Randić matrix of a mixed graph M and give the definitions of Hermitian-Randić characteristic polynomial and Hermitian-Randić energy of a mixed graph M. We give the bounds on the Hermitian-Randić energy of a mixed graph M with respect to its order, the Hermitian-Randić spectrum and a general Randić index (with (alpha=-1)).

In this paper, we define the Hermitian-Randić matrix of a mixed graph M and study some basic characteristics of the Hermitian-Randić matrix of mixed graphs.

Mixed Eulerian Sandwich ProblemInstance: Given mixed graphs H1= V,E1∪A1) and H2= V,E2∪A2) with E1⊆E2,A1⊆A2.

Shang etc. [ 27] proposed an exact graph isomorphism algorithm based on circuit simulation method, which is mainly used in a directed graph, undirected graph and mixed graph (refers as a mixture of directed graph or undirected graph).

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