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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 ...
An incidence in a graph is a vertex-edge pair such that the vertex is an endpoint of the edge. incidence matrix The incidence matrix of a graph is a matrix whose rows are indexed by vertices of the graph, and whose columns are indexed by edges, with a one in the cell for row i and column j when vertex i and edge j are incident, and a zero ...
The edge is said to join and and to be incident on and on . A vertex may exist in a graph and not belong to an edge. Under this definition, multiple edges, in which two or more edges connect the same vertices, are not allowed.
The edge is said to join x and y and to be incident on x and on y. A vertex may exist in a graph and not belong to an edge. The edge (y, x) is called the inverted edge of (x, y). Multiple edges, not allowed under the definition above, are two or more edges with both the same tail and the same head.
An edge-graceful labeling on a simple graph without loops or multiple edges on p vertices and q edges is a labeling of the edges by distinct integers in {1, …, q} such that the labeling on the vertices induced by labeling a vertex with the sum of the incident edges taken modulo p assigns all values from 0 to p − 1 to the vertices.
Formally, an edge cover of a graph G is a set of edges C such that each vertex in G is incident with at least one edge in C. The set C is said to cover the vertices of G. The following figure shows examples of edge coverings in two graphs (the set C is marked with red). A minimum edge covering is an edge
If you've been having trouble with any of the connections or words in Wednesday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further down.
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 .