#### 228 Citations

The recognition of Series Parallel digraphs

- Computer Science, Mathematics
- STOC
- 1979

An algorithm is presented that recognizes the class of General Series Parallel digraphs and runs in time proportional to the size of its input and calculates the transitive reduction and transitive closure of any General Series parallel digraph. Expand

Connection digraphs and second-order line digraphs

- Computer Science, Mathematics
- Discret. Math.
- 1982

A directed analogue of the concept of an intersection graph, defined for collections of ordered pairs of sets and called the connection digraph, is used to achieve the primary result. Expand

When a digraph and its line digraph are connected and cospectral

- Computer Science, Mathematics
- Discret. Math.
- 1998

All digraphs each one of which is cospectral with its line digraph and both the Digraph and its lineDigraph are connected are characterized and it is seen that there are arbitrarily large sets of cospectrals. Expand

The Underlying Graph of a Line Digraph

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1992

The location of loops and digons are determined, and save for a few exceptions, the solution is unique up to converses, and the relation between the automorphism groups of a line digraph and its underlying graph follows as a corollary. Expand

The of a ying graph line digraph *

- 2001

Villar, J.L., The underlying graph of a line digraph, Discrete Applied Mathematics 37/38 (1992) 525-538. The recovery of a line digraph from its underlying graph is considered in this paper. The… Expand

Optimal constructions of reversible digraphs

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1984

The algorithms may be used as approximate methods for finding a PERT network with the minimum number of dummy activities when finding a minimum homeomorph and a minimum split of a digraph which are line digraphs. Expand

Algebraic properties of a digraph and its line digraph

- Mathematics, Computer Science
- J. Interconnect. Networks
- 2003

The spectra of those matrices are studied and a relationship between their characteristic polynomials is obtained that allows us to relate properties of G and LG, specifically the number of cycles of a given length. Expand

Line digraphs and coreflexive vertex sets

- Computer Science, Mathematics
- Discret. Math.
- 1998

The concept of coreflexive set is introduced to study the structure of digraphs and leads to another natural way of forming an intersection digraph from a given digraph. Expand

On-Line Algorithms for Orders

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 1997

This paper presents this “on-line” algorithmics on posets and surveys the main results obtained under this approach. Expand

A Labeling Algorithm to Recognize a Line Digraph and Output its Root Graph

- Mathematics, Computer Science
- Inf. Process. Lett.
- 1982

A very efficient, linear time algorithm for the recognition of line digraphs based on a reformulation of the characterization of line Digraphs proved by Harary and Norman is presented. Expand

#### References

SHOWING 1-2 OF 2 REFERENCES

The number of functional digraphs

- Mathematics
- 1959

Our object is to find a generating function whose coefficients give the number of isomorphism types of functional digraphs with a given finite number of points. I t will be seen that functional… Expand

Congruent Graphs and the Connectivity of Graphs

- Mathematics
- 1932

We give here conditions that two graphs be congruent and some theorems on the connectivity of graphs, and we conclude with some applications to dual graphs. These last theorems might also be proved… Expand