Title: Discrete-Time Open Quantum Walks for Vertex Ranking in Graphs

Abstract: This article utilizes the inspiration to apply the Wyel operators for producing the Kraus operators, which are crucial in the discrete-time open quantum walk. It assists us in extending the idea of discrete-time open quantum walk on arbitrary directed and undirected graphs. We make the new model of quantum walk useful to build up a quantum PageRank algorithm. In classical computation, Google's PageRank is a significant algorithm for arranging web pages on the World Wide Web. In general, it is also a fundamental measure for quantifying the importance of vertices in a network. Similarly, the new quantum PageRank also represents the importance of the vertices of a network. We can compute the new quantum PageRank algorithm in polynomial time using a classical computer. We compare the classical PageRank and the newly defined quantum PageRank for different types of complex networks, such as the scale-free network, Erdos-Renyi random network, Watts-Strogatz network, spatial network, Zachary Karate club network, random-k-out graph, binary tree graph, GNC network, Barabasi and Albert network, etc.