Sinha Deepa, Sethi Anshu
South Asian University Akbar Bhawan, Chanakyapuri, New Delhi 110 021 India.
Center For Mathematical Sciences, Banasthali University, Banasthali, 304 022 Rajasthan India.
Springerplus. 2015 Nov 17;4(1):704. doi: 10.1186/s40064-015-1499-0. eCollection 2015.
A (or in short) is a graph in which each edge carries a value [Formula: see text] called its denoted specially as [Formula: see text]. Given a sigraph , = () called the of is that sigraph in which edges of are represented as , two of these vertices are defined to be adjacent whenever the corresponding edges in have a vertex in common and any such edge is defined to be whenever both and are negative edges in . Here is called of . [Formula: see text] = [Formula: see text] [Formula: see text] [Formula: see text], := [Formula: see text] is defined similarly. In this paper, we give an algorithm to obtain iterated line sigraph and detect for which value of '' it is and determine its complexity. In the end we will propose a technique that will use adjacency matrix of and adjacency matrix of [Formula: see text] which is balanced for some '' as a parameter to encrypt a network and forward the data in the form of balanced [Formula: see text] and will decrypt it by applying inverse matrix operations.
A（或简称为）是一个图，其中每条边都带有一个值[公式：见正文]，称为其 ，特别表示为[公式：见正文]。给定一个符号图 ， = () 称为 的 ，是这样一个符号图，其中 的边表示为 ，只要 中的相应边有一个公共顶点，这两个顶点就被定义为相邻，并且只要 和 在 中都是负边，任何这样的边 就被定义为 。这里 称为 的 。[公式：见正文] = [公式：见正文] [公式：见正文] [公式：见正文]， := [公式：见正文] 类似地定义。在本文中，我们给出一种算法来获得迭代线符号图，并检测对于哪个 '' 值它是 ，并确定其复杂度。最后，我们将提出一种技术，该技术将使用 的邻接矩阵和对于某些 '' 是平衡的[公式：见正文]的邻接矩阵作为参数来加密网络，并以平衡的[公式：见正文]形式转发数据，并通过应用逆矩阵运算来解密它。
