• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.257-268
• /
• 2007

An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertex $v_i$ in an oriented graph D is $a_{v_i}\;(or\;simply\;a_i)=n-1+d_{v_i}^+-d_{v_i}^-,\;where\; d_{v_i}^+\;and\;d_{v_i}^-$ are the outdegree and indegree, respectively, of $v_i$ and n is the number of vertices in D. In this paper, we give a new proof of Avery's theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.22 no.6
• /
• pp.91-97
• /
• 2022

There is hare and tortoise racing algorithm(HTA) for single-source(SS) singly linked list(SLL) with O(n) time complexity. But the fast method is unknown for general graph with multi-source, multi-destination, and multi-branch(MSMDMB). This paper suggests linear time cycle detection algorithm for given undirected and digraph with MSMDMB. The proposed method reduced the given graph G contained with unnecessary vertices(or nodes) to cycle into reduced graph G' with only necessary vertices(or nodes) to cycle based on the condition of cycle formation. For the reduced graph G', we can be find the cycle set C and cycle length λ using linear search within linear time. As a result of experiment data, the proposed algorithm can be obtained the cycle for whole data.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.7
• /
• pp.893-900
• /
• 2007

This paper suggests an algorithm that improves the disadvantages of the Dijkstra algorithm that is commonly used in GPS navigation system, searching for the shortest path. Dijkstra algorithm, first of all, requires much memory for the performance of the algorithm. It has to carry out number of node minus 1, since it determines the shortest path from all the nodes in the graph, starting from the first node. Therefore, Dijkstra algorithm might not be able to provide the information on every second, searching for the shortest path between the roads of the congested city and the destination. In order to solve these problems, this paper chooses a method of searching a number of nodes at once by means of choosing the shortest path of all the path nodes (select of minimum weight arc in-degree and out-degree), excluding the departure and destination nodes, and of choosing all the arcs that coincide with the shortest path of the path nodes, from all the node outgoing arcs starting from the departure node. On applying the suggested algorithm to 14 various digraphs, we succeeded to search the shortest path. In addition, the result was obtained at the speed of 2 to 3 times faster than that of Dijkstra algorithm, and the memory required was less than that of Dijkstra algorithm.