The topological structure of a network can be described by a connected graph \(G = (V, E)\) where V(G) is a set of nodes to be connected and E(G) is a set of direct communication links between the nodes. A physical connection between the different components of a parallel system is provided by an interconnection network. Many graph theoretic parameters are used to study the efficiency and reliability of an interconnection network. A set \(S \subseteq V(G)\) is said to be secure if the security condition, for every \(X \subseteq S\), \(\left| N[X] \cap S\right| \ge \left| N[X] - S\right| \) holds. Now, a set \(S \subseteq V(G)\) is secure dominating, if it is both secure and dominating. The secure domination number of G, is the minimum cardinality of a secure dominating set in G. In the current era, security is definitely a desirable property for the interconnection networks and hence these type of study has wide applications. In this paper, we have studied the security number and secure domination number of Honeycomb Networks.

中文翻译：

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安全地控制蜂窝网络

网络的拓扑结构可以用连接图\（G =（V，E）\）来描述，其中V（G）是要连接的节点的集合，而E（G）是之间的直接通信链路的集合节点。并行系统的不同组件之间的物理连接由互连网络提供。许多图论参数用于研究互连网络的效率和可靠性。如果安全条件对每个\（X \ subseteq S \），\（\ left | N [X] \ cap S \ right | \是安全条件，则说集合\（S \ subseteq V（G）\）是安全的。 ge \ left | N [X]-S \ right | \）成立。现在，集合\（S \ subseteq V（G）\）是安全的，如果它既安全又占主导地位。所述的安全控制数ģ，是在安全控制集的最小基数ģ。在当前时代，安全性绝对是互连网络的理想属性，因此这类研究具有广泛的应用。在本文中，我们研究了蜂窝网络的安全号和安全控制号。