Graph in Tree, Cycle in Cycle, Spiral Graph, and More
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A MetaGraph is a higher-level graph whose vertices are themselves graphs, with edges representing specified relations among these graphs. An Iterated MetaGraph extends this notion recursively: its vertices are MetaGraphs, thereby forming a hierarchical structure of graphs-of-graphs across multiple levels. In this paper, we introduce and study specific classes of MetaGraphs, including Graph-in-Tree and Cycle-in-Cycle structures. In addition, we define a new class of graphs, called Spiral Graphs, and investigate their fundamental properties.