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292:. A labeled vertex is a vertex that is associated with extra information that enables it to be distinguished from other labeled vertices; two graphs can be considered isomorphic only if the correspondence between their vertices pairs up vertices with equal labels. An unlabeled vertex is one that can be substituted for any other vertex based only on its
397:. Collection Universitaire de Mathématiques, II Dunod, Paris 1958, viii+277 pp. (English edition, Wiley 1961; Methuen & Co, New York 1962; Russian, Moscow 1961; Spanish, Mexico 1962; Roumanian, Bucharest 1969; Chinese, Shanghai 1963; Second printing of the 1962 first English edition. Dover, New York 2001)
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consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another.
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of a polyhedron forms a graph, the vertices of which are the vertices of the polyhedron, but polyhedron vertices have additional structure (their geometric location) that is not assumed to be present in graph theory. The
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is a vertex with degree zero; that is, a vertex that is not an endpoint of any edge (the example image illustrates one isolated vertex). A
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The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex
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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
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is a collection of vertices the removal of which would disconnect the remaining graph into small pieces. A
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From the point of view of graph theory, vertices are treated as featureless and indivisible
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is a set of vertices that includes at least one endpoint of each edge in the graph. The
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of a vertex in a polyhedron is analogous to the neighborhood of a vertex in a graph.
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if it has symmetries that map any vertex to any other vertex. In the context of
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of a vertex, denoted 𝛿(v) in a graph is the number of edges incident to it. An
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is a graph in which the vertices represent concepts or classes of objects.
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is a vertex the removal of which would disconnect the remaining graph; a
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Example network with 8 vertices (of which one is isolated) and 10 edges.
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Gallo, Giorgio; Pallotino, Stefano (1988). "Shortest path algorithms".
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is a vertex that is adjacent to every other vertex in the graph.
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Vertices in graphs are analogous to, but not the same as,
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in the graph and not based on any additional information.
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is a set of vertices no two of which are adjacent, and a
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vertices always leaves the remaining graph connected. An
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is the fundamental unit of which graphs are formed: an
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Biggs, Norman; Lloyd, E. H.; Wilson, Robin J. (1986).
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of the graph, formed by all vertices adjacent to
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455:. Reading, Mass.: Addison-Wesley Publishing.
131:consists of a set of vertices and a set of
27:Fundamental unit of which graphs are formed
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158:is said to be adjacent to another vertex
87:Learn how and when to remove this message
470:Harary, Frank; Palmer, Edgar M. (1973).
253:is a graph in which removing fewer than
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50:This article includes a list of general
395:Théorie des graphes et ses applications
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364:Annals of Operations Research
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474:. New York, Academic Press.
433:. Oxford : Clarendon Press.
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408:Introductory graph theory
332:Glossary of graph theory
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430:Graph theory, 1736-1936
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472:Graphical enumeration
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109:discrete mathematics
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498:Weisstein, Eric W.
376:10.1007/BF02288320
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282:graph isomorphism
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370:(1): 1–79.
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69:introducing
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451:(1969).
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119:(plural
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