Abstract
This paper investigates pseudographs with degree sequences which have infinitely many terms greater than 1. Two nonisomorphic pseudographs with the same degree sequence are adjacent if one can be obtained from the other by an elementary operation called switching. With this notion of adjacency we can regard distinct pseudographs with the same degree sequence as the vertices of a graph, called the graph of pseudographic realizations of that sequence. Some results concerning the nature of the components of such graphs of realizations have already been obtained. We add to these results here and, in particular, determine all cases in which the graph has a component which is a path, and all cases in which it has an endvertex.
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Reference
R.B. Eggleton and D.A. Holton, The graph of type (0,∞,∞) realizations of a graphic sequence, Combinatorial Mathematics VI, Lecture Notes in Maths. 748 (Springer-Verlag, 1979), 40–54.
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© 1980 Springer-Verlag
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Eggleton, R.B., Holton, D.A. (1980). Pseudographic realizations of an infinitary degree sequence. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088904
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DOI: https://doi.org/10.1007/BFb0088904
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