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Class-reconstruction of total graphs

โœ Scribed by David W. Bange; Anthony E. Barkauskas; Linda H. Host

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
533 KB
Volume
11
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

โœฆ Synopsis

It is shown that given any vertex-deleted total graph, every reconstruction into a total graph by the addition of a vertex yields the original total graph. The proof indicates how the reconstruction can be done. Hu, for i = 1 , . . . , p , then G Definition. Let C be a class of graphs. A graph G E C with V ( C ) = { u , , . . . , u p } is said to be class-reconstriictible from 11 subgraphs if whenever

๐Ÿ“œ SIMILAR VOLUMES

Reconstruction of infinite graphs
Reconstruction of infinite graphs
โœ C.St.J.A. Nash-Williams ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 929 KB

The paper recalls several known results concerning reconstruction and edge-reconstruction of infinite graphs, and draws attention to some possibly interesting unsolved problems.

The total interval number of a graph, I:
The total interval number of a graph, I: Fundamental classes
โœ Thomas M. Kratzke; Douglas B. West ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 906 KB

Kratzke, T.M. and D.B. West, The total interval number of a graph, I: Fundamental classes, Discrete Mathematics 118 (1993) 145-156. A multiple-interval representation of a simple graph G assigns each vertex a union of disjoint real intervals, such that vertices are adjacent if and only if their assi

Reconstructibility versus edge reconstru
Reconstructibility versus edge reconstructibility of infinite graphs
โœ Carsten Thomassen ๐Ÿ“‚ Article ๐Ÿ“… 1978 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 151 KB

## RECONgTRUCTIBILITY VERSUI~ EDGE RECONSTR1UCTIBILtlY OF !NF![?CTE GN~APNS Cars,~en -FI-!Ob,~ ASSEN A.hah,,\*~atL~k /~.t;tir~\*., t h~ieersi;e~sp ~tk~'n, S0{P} Aarbus C. Detm~a& Rcc~ .d 23 [;cccm~cr 1~)77 [~ยข :{>.cd 7 April D)TS For every cm~dma! a >R o ~here exi::ts an ,:t-rQ,',ular .g;api~ w[?

Computer reconstruction of small graphs
Computer reconstruction of small graphs
โœ B. D. McKay ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 114 KB

## Abstract The Reconstruction Conjecture is established for graphs with nine vertices.