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To test the effectivity of this approach at global scales, Instagram posts from fourteen natural areas were selected to analyse the emergent discourse around these areas. The use of Graph Theory on social media data is a promising approach to identify emergent properties of the complex physical and cognitive interactions that occur between humans and nature. Then,(i)There is an -path (respectively, an -path) containing all vertices of, and(ii)For each -path, , i.e., misses at least one vertex from. Tutte constructed the Tutte fragment, a triangle-free 3-leg fragment with 15 vertices, and showed the following statement. In 1880, Tait conjectured that a 3-connected cubic plane graph has a Hamilton cycle. įinding Hamilton cycles in graphs is a famous topic in graph theory. A Hamilton cycle of a graph is a cycle containing all vertices of. A -leg fragment is a connected plane graph such that there are exactly vertices of with degree two, and the remaining vertices have degree three. A graph is -connected if, and for any of size, a graph is connected. A graph is connected if there is a -path for all distinct. The triangle is a cycle of length 3, and a graph is triangle-free if it contains no triangle. Similar to -path, a cycle of a graph is defined as a sequence of distinct vertices, of such that, , for all. An -path of a graph is a sequence of distinct vertices of such that, for all. A plane graph is a graph embedded in a plane without edge crossing. A graph is cubic if all vertices have degree exactly three. The degree of a vertex is the number of edges incident to. Let = (, ) be a graph, where is the vertex set of and is the edge set of. We consider only simple undirected graph.
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Recently, it is combined with fixed point theory in. Graph theory can be combined together with other branches of mathematics such as algebraic graph theory, matroid theory, graph labeling, and topological graph theory. In chemistry and biology, it gives an illustration of molecular structures in, and it identifies interactions between humans and nature in. Graph theory has applications in various research areas. In this paper, we show that an upper bound of is for. The circumference of a graph is the length of a longest cycle in, denoted by.