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The (m,n)-lollipop graph is the graph obtained by joining a complete graph K_m to a path graph P_n with a bridge. Precomputed properties of lollipop graphs are available in ...

A graph G is distance transitive if its automorphism group is transitive on pairs of vertices at each pairwise distance in the graph. Distance-transitivity is a ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

A topological space X is pathwise-connected iff for every two points x,y in X, there is a continuous function f from [0,1] to X such that f(0)=x and f(1)=y. Roughly speaking, ...

A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

The banner graph is the (4,1)-tadpole graph illustrated above. It could perhaps also be termed the 'P graph.' It is implemented in the Wolfram Language as ...

The longhorn graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["LonghornGraph"].

A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the ...

A set which is connected but not simply connected is called multiply connected. A space is n-multiply connected if it is (n-1)-connected and if every map from the n-sphere ...