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A vertex with degree 1 is called a leaf vertex or end vertex or a pendant vertex, and the edge incident with that vertex is called a pendant edge. In the graph on the right, {3,5} is a pendant edge. This terminology is common in the study of trees in graph theory and especially trees as data structures. A vertex with degree n − 1 in a graph ...
An angle bisector of a triangle is a straight line through a vertex that cuts the corresponding angle in half. The three angle bisectors intersect in a single point, the incenter, which is the center of the triangle's incircle. The incircle is the circle that lies inside the triangle and touches all three sides. Its radius is called the inradius.
Formann et al. (1993) observed that every straight-line drawing of a graph with maximum degree d has angular resolution at most 2π/d: if v is a vertex of degree d, then the edges incident to v partition the space around v into d wedges with total angle 2π, and the smallest of these wedges must have an angle of at most 2π/d.
The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices. In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 .
A YΔ-transformation removes a degree-three vertex from a graph, adding edges between all of its former neighbors if those edges did not already exist; the reverse transformation, a ΔY-transformation, removes the edges of a triangle from a graph and replaces them by a new degree-three vertex adjacent to the same three vertices.
For a simple graph with vertex set U = {u 1, …, u n}, the adjacency matrix is a square n × n matrix A such that its element A ij is 1 when there is an edge from vertex u i to vertex u j, and 0 when there is no edge. [1] The diagonal elements of the matrix are all 0, since edges from a vertex to itself are not
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 ...
where the degree of a vertex counts the number of times an edge terminates at that vertex. In an undirected graph , this means that each loop increases the degree of a vertex by two. In a directed graph , the term degree may refer either to indegree (the number of incoming edges at each vertex) or outdegree (the number of outgoing edges at ...