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A graph with 16 vertices and six bridges (highlighted in red) An undirected connected graph with no bridge edges. In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
Microsoft Graph supports many different types of charts, but its output is dated. Office 2003 was the last version to use Microsoft Graph for hosting charts inside Office applications as OLE objects. Office 2007 – specifically, Excel 2007 – includes a new integrated charting engine, and the charts are native to the applications. The new ...
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
A graph G which is connected but not 2-connected is sometimes called separable. Analogous concepts can be defined for edges. In the simple case in which cutting a single, specific edge would disconnect the graph, that edge is called a bridge. More generally, an edge cut of G is a set of edges whose removal renders the graph disconnected.
In a connected graph that is not a theta graph, peripheral cycles cannot have chords, because any chord would be a bridge, separated from the rest of the graph. In this case, C {\displaystyle C} is peripheral if it is an induced cycle with the property that the subgraph G ∖ C {\displaystyle G\setminus C} formed by deleting the edges and ...
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A directed graph or digraph is a graph in which edges have ... The Königsberg Bridge problem. ... Graph theory tutorial Archived 2012-01-16 at the Wayback Machine;