Volume 34, Issue 2
On Potentially Graphical Sequences of G−E(H)

Bilal A. Chat and S. Pirzada

10.4208/ata.2018.v34.n2.8

Anal. Theory Appl., 34 (2018), pp. 187-198.

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  • Abstract

A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a (a,b,n)-graph. A (b,b,n)-graph is called (b,n)-graph and is denoted by Kbn(it is a complete graph), its complement by Kbn. A non increasing sequence π = (d1,···,dn) of nonnegative integers is said to be (a,b,n) graphic if it is realizable by an (a,b,n)-graph. We say a simple graphic sequence π = (d1,···,dn) is potentially K4−K2∪K2-graphic if it has a a realization containing an K4−K2∪K2 as a subgraph where K4 is a complete graph on four vertices and K2∪K2 is a set of independent edges. In this paper, we find the smallest degree sum such that every n-term graphical sequence contains K4−K2∪K2 as subgraph.

  • History

Published online: 2018-07

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