DOT is a plain text graph description language primarily used for representing directed and undirected graphs. It is part of the Graphviz software suite, which is an open-source graph visualization tool. DOT allows users to specify the nodes and edges of a graph in a simple syntax, making it easy to define graph structures programmatically.

The concept of a "bondage number" typically arises in the context of graph theory. Specifically, the bondage number of a graph is defined as the minimum number of edges that must be removed from the graph in order to make it impossible to maintain a dominating set—that is, a set of vertices such that every vertex in the graph is either in the dominating set or is adjacent to a vertex in the dominating set—of a certain size.

Closeness centrality is a measure used in network analysis to determine how central or important a particular node (vertex) is within a graph. The idea behind closeness centrality is that nodes that are closer to all other nodes in the network are more central than those that are farther away. This metric is particularly useful for understanding the efficiency of spreading information or resources through the network.

A "Friendly index set" isn't a standard term widely recognized in mathematics or related fields as of my last update. However, it might be a term or concept from a specific domain, such as computer science, game theory, or a niche area of mathematics.

A **bipartite double cover** of a graph is a specific type of covering graph that is particularly relevant in the context of bipartite graphs. To elaborate, consider the following concepts: 1. **Bipartite Graphs**: A bipartite graph is a graph that can be divided into two disjoint sets of vertices \( U \) and \( V \) such that every edge connects a vertex in \( U \) to a vertex in \( V \).

"Bipartite half" might refer to concepts within graph theory, particularly regarding bipartite graphs. A **bipartite graph** is a type of graph where the set of vertices can be divided into two distinct sets such that no two graph vertices within the same set are adjacent.

Time-sharing systems represent a significant evolution in computing, allowing multiple users to interact with a computer simultaneously. This concept emerged from the need for more efficient use of computing resources, which were, at the time, expensive and limited. ### Key Stages in the Evolution of Time-Sharing Systems: 1. **Early Computing (1950s)**: - Computers were large, expensive, and primarily used for batch processing.

In graph theory, the complement of a graph is a graph that contains the same set of vertices but has edges that are not present in the original graph.

A Type-in program refers to a type of computer program where the user is expected to manually enter (or "type in") the code into a computer or programming environment. This practice was particularly popular in the early days of personal computing, especially in the 1980s and 1990s, when magazines and books would publish source code listings for users to type into their own computers. Type-in programs often serve as a way to teach programming concepts, allowing users to learn by doing.

Chordal completion, also known as chordal graph completion, refers to the process of transforming a given graph into a chordal graph. A chordal graph (or "perfect graph") is defined as a graph in which every cycle of four or more vertices has a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. The process of chordal completion involves adding edges to the original graph in such a way that the resulting graph becomes chordal.

The common ones.

In graph theory, a **cycle** is a path that starts and ends at the same vertex, with all other vertices in the path being distinct. More formally, a cycle in an undirected graph is defined as a sequence of vertices \( v_1, v_2, ...

An edge cycle cover in graph theory is a collection of cycles that covers every edge of a graph exactly once. In other words, it is a set of cycles in which each edge of the graph is included in exactly one of the cycles. This concept is particularly relevant in the study of Eulerian paths and circuits.

Advanced Network and Services (ANS) is a nonprofit organization that focuses on promoting and advancing the development of high-performance networking and advanced services for educational, research, and other institutions. It plays a significant role in the development of cutting-edge network technologies and services that facilitate collaboration and innovation in various fields, including education, science, and information technology. ANS often collaborates with universities, government agencies, and industry partners to foster research and development in networking technologies.

Al Gore, the former Vice President of the United States, is known for his advocacy on environmental issues and climate change, but he also has a significant connection to information technology. In the 1990s, while serving under President Bill Clinton, Gore promoted the development of the Internet, referring to it as "The Information Superhighway." He championed initiatives that contributed to the expansion and accessibility of the Internet, including federal funding for research and development in information technology.

As of my last knowledge update in October 2021, Barry Appelman does not appear to be a widely recognized figure in literature, politics, entertainment, or other public domains. It's possible that he could be a private individual, a professional in a specific field, or someone who has gained recognition after my last update.