# An Algorithm to Detect Cycle in an Undirected Graph

## Related Articles

- SOME REMARKS ON THE STRUCTURE OF STRONG k-TRANSITIVE DIGRAPHS. HERNÁNDEZ-CRUZ, CÉSAR; MONTELLANO-BALLESTEROS, JUAN JOSÉ // Discussiones Mathematicae: Graph Theory;2014, Vol. 34 Issue 4, p651
A digraph D is k-transitive if the existence of a directed path (v0, v1, ..., vk), of length k implies that (v0, vk) âˆˆ & A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an...

- THE i-CHORDS OF CYCLES AND PATHS. MCKEE, TERRY A. // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p607
An i-chord of a cycle or path is an edge whose endpoints are a distance i â‰¥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results...

- 3-TRANSITIVE DIGRAPHS. Hernández-Cruz, César // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p205
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u; v;w; x) of length 3 in D implies the existence of the arc (u, x) âˆˆ A(D). In this article strong 3-transitive digraphs are...

- ON MONOCHROMATIC PATHS AND BICOLORED SUBDIGRAPHS IN ARC-COLORED TOURNAMENTS. DELGADO-ESCALANTE, PIETRA; GALEANA-SANCHEZ, HORTENSIA // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p791
Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n âˆˆ N such that there is a monochromatic directed path from v to n....

- Î³-CYCLES AND TRANSITIVITY BY MONOCHROMATIC PATHS IN ARC-COLOURED DIGRAPHS. CASAS-BAUTISTA, ENRIQUE; GALEANA-SÁNCHEZ, HORTENSIA; ROJAS-MONROY, ROCÍO // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 3, p493
We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a âˆˆ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A Î³-cycle in D is a...

- The Spectrum of Tetrahedral Quadruple Systems. Wang, Jian; Liang, Miao; Du, Beiliang // Graphs & Combinatorics;Jul2011, Vol. 27 Issue 4, p593
n ordered analogue of quadruple systems is tetrahedral quadruple systems. A tetrahedral quadruple system of order v and index Î», TQS( v, Î»), is a pair $${(S, \mathcal{T})}$$ where S is a finite set of v elements and $${\mathcal{T}}$$ is a family of oriented tetrahedrons of elements of S...

- SOME RESULTS ON SEMI-TOTAL SIGNED GRAPHS. SINHA, DEEPA; GARG, PRAVIN // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p625
A signed graph (or sigraph in short) is an ordered pair S = (SuÎ´), where Su is a graph G = (V,E), called the underlying graph of S and Î´ : E â†’ {+,-} is a function from the edge set E of Suinto the set {+,-}, called the signature of S. The x-line sigraph of S denoted by L x (S) is a...

- On Strongly Regular Graphs with /m2 - m3/ â‰¤ 3. Lepović, Mirko // Global Journal of Pure & Applied Mathematics;2010, Vol. 6 Issue 2, p125
We say that a regular graph G of order n and degree r â‰¥ 1 (which is not the complete graph) is strongly regular if there exist non-negative integers Ï„ and Î¸ such that /Si âˆ© Sj / = Ï„ for any two adjacent vertices I and j , and /SI âˆ© Sj/= Î¸ for any two distinct...

- New Ore's Type Results on Hamiltonicity and Existence of Paths of Given Length in Graphs. Lichiardopol, Nicolas // Graphs & Combinatorics;Jan2013, Vol. 29 Issue 1, p99
The well-known Ore's theorem (see Ore in Am Math Mon 65:55, ), states that a graph G of order n such that d( x) + d( y) â‰¥ n for every pair { x, y} of non-adjacent vertices of G is Hamiltonian. In this paper, we considerably improve this theorem by proving that in a graph G of order n and...