Nagoor Gani A, Latha S R
PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020 India.
Department of Mathematics, Sona College of Technology (Autonomous), Salem, Tamil Nadu 636 005 India.
Springerplus. 2016 Oct 22;5(1):1854. doi: 10.1186/s40064-016-3473-x. eCollection 2016.
A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines.
图中的哈密顿回路是指恰好访问每个节点/顶点一次的回路。包含哈密顿回路的图称为哈密顿图。已经有多项研究致力于找出哈密顿图中哈密顿回路的数量。随着顶点和边的数量增加，要追踪顶点之间所有不同的连接方式变得非常困难。因此，借助将图解释为矩阵的计算机系统，可以有效地对大型图进行分析。当然，一个优秀且编写良好的算法会使分析速度更快。快速测试两个顶点之间是否存在边的最便捷方法是使用邻接矩阵来表示图。本文提出了一种新算法，利用邻接矩阵和模糊图顶点的度来寻找模糊哈密顿回路。还对模糊图结构进行了建模，以用靛蓝航空选定的航空网络来说明所提出的算法。
