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In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
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 vertex separator S in G is minimal if and only if the graph G – S, obtained by removing S from G, has two connected components C 1 and C 2 such that each vertex in S is both adjacent to some vertex in C 1 and to some vertex in C 2.
The universal covering graph T of a connected graph G can be constructed as follows. Choose an arbitrary vertex r of G as a starting point. Each vertex of T is a non-backtracking walk that begins from r, that is, a sequence w = (r, v 1, v 2, ..., v n) of vertices of G such that v i and v i+1 are adjacent in G for all i, i.e., w is a walk
Graph = with the -axis as the horizontal axis and the -axis as the vertical axis.The -intercept of () is indicated by the red dot at (=, =).. In analytic geometry, using the common convention that the horizontal axis represents a variable and the vertical axis represents a variable , a -intercept or vertical intercept is a point where the graph of a function or relation intersects the -axis of ...
The vertex space of G is the vector space over the finite field of two elements /:= {,} of all functions /. Every element of V ( G ) {\displaystyle {\mathcal {V}}(G)} naturally corresponds the subset of V which assigns a 1 to its vertices.
The edge-connectivity of a connected vertex-transitive graph is equal to the degree d, while the vertex-connectivity will be at least 2(d + 1)/3. [1] If the degree is 4 or less, or the graph is also edge-transitive, or the graph is a minimal Cayley graph, then the vertex-connectivity will also be equal to d. [4]
Example graph that has a vertex cover comprising 2 vertices (bottom), but none with fewer. In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem.