Histories in path graphs

• Autorzy: Ludovít Niepel
• Języki publikacji: EN

Abstrakty

EN

For a given graph G and a positive integer r the r-path graph, $P_r(G)$, has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length r-1, and their union forms either a cycle or a path of length k+1 in G. Let $P^k_r(G)$ be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgraph of $P^k_r(G)$. The k-history $P^{-k}_r(H)$ is a subgraph of G that is induced by all edges that take part in the recursive definition of H. We present some general properties of k-histories and give a complete characterization of graphs that are k-histories of vertices of 2-path graph operator.

Słowa kluczowe

EN

path-graph; graph dynamics; history

Kategorie tematyczne

• 05C75: Structural characterization of families of graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 2
• Strony: 345-357

Daty

wydano

2007

otrzymano

2006-05-15

poprawiono

2007-01-15

zaakceptowano

2007-01-15

Twórcy

autor

Ludovít Niepel

• Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

Bibliografia

• [1] R.E.L. Aldred, M.N. Ellingham, R. Hemminger and P. Jipsen, P₃-isomorphism for graphs, J. Graph Theory 26 (1997) 35-51, doi: 10.1002/(SICI)1097-0118(199709)26:1<35::AID-JGT5>3.0.CO;2-I
• [2] C. Balbuena and D. Ferrero, Edge-connectivity and super edge-connectivity of P₂-path graphs, Discrete Math. 269 (2003) 13-20, doi: 10.1016/S0012-365X(02)00828-2.
• [3] C. Balbuena and P. García-Vázquez, Edge-connectivity in Pₖ-path graphs, Discrete Math. 286 (2004) 213-218, doi: 10.1016/j.disc.2004.05.007.
• [4] H.J. Broersma and C. Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444, doi: 10.1002/jgt.3190130406.
• [5] D. Ferrero, Edge connectivity of iterated P₃-path graphs, Congr. Numer. 155 (2002) 33-47.
• [6] D. Ferrero, Connectivity of path graphs, Acta Mathematica Universitatis Comenianae LXXII (1) (2003) 59-66.
• [7] M. Knor and L. Niepel, Diameter in iterated path graphs, Discrete Math. 233 (2001) 151-161, doi: 10.1016/S0012-365X(00)00234-X.
• [8] M. Knor and L. Niepel, Centers in path graphs, JCISS 24 (1999) 79-86.
• [9] M. Knor and L. Niepel, Independence number in path graphs, Computing and Informatics 23 (2004) 179-187.
• [10] H. Li and Y. Lin, On the characterization of path graphs, J. Graph Theory 17 (1993) 463-466, doi: 10.1002/jgt.3190170403.
• [11] X. Li, Isomorphism of P₃-graphs, J. Graph Theory 21 (1996) 81-85, doi: 10.1002/(SICI)1097-0118(199601)21:1<81::AID-JGT11>3.0.CO;2-V
• [12] L. Niepel, M. Knor and L. Soltés, Distances in iterated line graphs, Ars Combin. 43 (1996) 193-202.
• [13] E. Prisner, Graph dynamics, Pitman Research Notes in Mathematics Series Vol 338 (Longman, Essex, 1995).
• [14] E. Prisner, Recognizing k-path graphs, Discrete Appl. Math. 99 (2000) 169-181, doi: 10.1016/S0166-218X(99)00132-8.
• [15] E. Prisner, The dynamics of the line and path graph operators, Discrete Math. 103 (1992) 199-207, doi: 10.1016/0012-365X(92)90270-P.
• [16] X. Yu, Trees and unicyclic graphs with hamiltonian path graphs, J. Graph Theory 14 (1990) 705-708, doi: 10.1002/jgt.3190140610.

Identyfikatory

DOI

10.7151/dmgt.1366