A bridged graph is a graph that contains one or more graph bridges. Examples of bridged graphs include path graphs,
ladder rung graphs, the bull
graph, star graphs, and trees.
A graph that is not bridged is said to be bridgeless. A connected bridgeless graph can be tested for in the Wolfram
Language using Not[KEdgeConnectedGraphQ[g,
2]] or EdgeConnectivity[g]
The numbers of simple bridged graphs on , 2, ... vertices are 0, 1, 2, 6, 18, 79, 462, 4344, ...
The numbers of simple connected bridged graphs on , 2, ... vertices are 0, 1, 1, 3, 10, 52, 351, 3714, 63638,
1912203, ... (OEIS A052446).
See alsoBridgeless Graph
, k-Edge-Connected Graph
Explore with Wolfram|Alpha
ReferencesSloane, N. J. A. Sequences A052446 and A263915 in "The On-Line Encyclopedia
of Integer Sequences."
Referenced on Wolfram|AlphaBridged Graph
Cite this as:
Weisstein, Eric W. "Bridged Graph." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BridgedGraph.html