In the
mathematicalMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
field of
graph theoryIn mathematics and computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a
path graph is a particularly simple example of a
treeIn mathematics, more specifically graph theory, a tree is a graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...
, namely one which is not branched at all, that is, contains only nodes of
degreeIn graph theory, the degree of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice. The degree of a vertex is denoted The maximum degree of a graph G, denoted by Δ, is the maximum degree of its vertices, and the minimum degree of a graph, denoted by δ, is...
two and one. In particular, two of its vertices have degree 1 and all others (if any) have degree 2.
Discussion
Ask a question about 'Path graph' Start a new discussion about 'Path graph' Answer questions from other users |
In the
mathematicalMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
field of
graph theoryIn mathematics and computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a
path graph is a particularly simple example of a
treeIn mathematics, more specifically graph theory, a tree is a graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...
, namely one which is not branched at all, that is, contains only nodes of
degreeIn graph theory, the degree of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice. The degree of a vertex is denoted The maximum degree of a graph G, denoted by Δ, is the maximum degree of its vertices, and the minimum degree of a graph, denoted by δ, is...
two and one. In particular, two of its vertices have degree 1 and all others (if any) have degree 2.