A graph is said to be reconstructible if it is determined up to isomorphism from the collection of all its one-vertex deleted unlabeled subgraphs.The reconstruction conjecture asserts that every graph G on at least 3 vertices is reconstructible. A graph G is paw-free if it contains no subgraph isomorphic to paw as induced subgraph. It is shown that 2-connected paw-free graphs G having no induced C4 or or C5 with diam(G) = 2 or diam(G) = diam() = 3 are reconstructible.
REFERENCES
1.
J. A.
Bondy
and R. L.
Hemminger
, “Graphreconstruction-a survey
”, J. Graph Theory
, 1
, 227
–268
(1977
).2.
J.A.
Bondy
, “A graph reconstructor's manual
”, in Surveys in Combinatorics, Proceedings of British Combinatorial Conference, London Mathematical Society Lecture Notes
, 116
, 221
–252
(1991
).3.
F.
Harary
, Graph Theory
, Addison-Wesley, Mass
., (1969
).4.
S. K.
Gupta
, Pankaj
Mangal
and Vineet
Paliwal
, “Some work towards the proofofthe reconstruction conjecture
", Discrete Math.
, 272
, 291
–296
(2003
).5.
B. D.
McKay
, “Smallgraphsarereconstructible
", Australas. J. Combin.
, 15
, 123
–126
(1997
).6.
S.
Ramachandran
and S.
Monikandan
, “Graph reconstruction conjecture: Reductions using complement, connectivity and distance
", Bull. Inst. Combin. Appl.
, 56
, 103
–108
(2009
),7.
W. T.
Tutte
, “AH the King's horses
", Graph Theory and related topics, Proceedings of the Conference held in honor of W. T. Tutte on the occasion of his 60th birthday
, edited by J.A. Bondyand U. S. R.
Murthy
, Academic Press
, New York
15
–33
(1976
).8.
Yang
Yongzhi
, “The reconstruction conjecture is true if all 2-connected graphs are reconstructible
", J. Graph Theory
, 12
, No. 2
, 237
–243
(1988
).
This content is only available via PDF.
© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
