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A Hasse diagram is a simple picture of a finite partially ordered set, forming a drawing of the partial order's transitive reduction. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from x to y precisely when x < y and there is no z such that x < z < y.
A basic example of a noncommutative vertex algebra is the rank 1 free boson, also called the Heisenberg vertex operator algebra. It is "generated" by a single vector b, in the sense that by applying the coefficients of the field b(z) := Y(b,z) to the vector 1, we obtain a spanning set.
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph. [2] In the abstract, all that matters is which pairs of vertices are connected by edges.
A graph drawing should not be confused with the graph itself (the abstract, non-visual structure) as there are several ways to structure the graph drawing. All that matters is which vertices are connected to which others by how many edges and not the exact layout. In practice, it is often difficult to decide if two drawings represent the same ...
A graceful labeling; vertex labels are in black and edge labels in red. A graph is known as graceful if its vertices are labeled from 0 to | E |, the size of the graph, and if this vertex labeling induces an edge labeling from 1 to | E |. For any edge e, the label of e is the positive difference between the labels of the two vertices incident ...
A gear graph, denoted G n, is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a wheel graph W n. Thus, G n has 2n+1 vertices and 3n edges. [4] Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs. [5]