Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Rao, A. R. (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

The class of self-complenentary egraphs has been extensively etudied by nany people, among others by C.R.J. Clephan, S.B, Rao, G, Ringel and H. Sache, and nany problems have been solved for this class, such as the Haniltonian problen and the characterisati on of potentially and forcibly self-complenentary dogree sequences (see [1], [2], [12), [13), [14, [15)). Thus self-complenentary graphs form an interesting class and this has been generalised by Hebbare [8] into the class of multipartite self-conplementary graphs.An r-partite self-complenentary graph is an r-partite graph G which is isomorphic to its r-partite complement where H has the sane vertex set as and is an edge of uv H iff u,v belong to different sets in the r-partition of G and is not an edge of G. A multipartite self-conplenentary graph is an r-partite self-conplenentary graph for scne r2 2. In this thesis we study the properties of multipartite self-comnlenantary aranhe complenentary graph are obtained as corollaries.The thesis is divided into two parts, In Part 1, which consists of the first five chapters, we study the propertics of r-partite self-complonentary graphs for general r. In Part II, consisting of the last two chapters, we study the demes ssences o hirartito sel1.mrlamentary sehe.In Chanter 1, we study the properties of complementing permutations of r-partite self-complementary graphs, In particular we prove that any complementing permutation of a connected bipartite self-complementary graph permutes the pertition sets as a whole and the square of any complementing permutation is an automornhism of the grous.


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This work is licensed under a Creative Commons Attribution 4.0 International License.


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