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

Bilal A. Chat & S. Pirzada

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

Published online: 2018-07

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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.

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@Article{ATA-34-187, author = {}, title = {On Potentially Graphical Sequences of G−E(H)}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {2}, pages = {187--198}, 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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2018.v34.n2.8}, url = {http://global-sci.org/intro/article_detail/ata/12586.html} }
TY - JOUR T1 - On Potentially Graphical Sequences of G−E(H) JO - Analysis in Theory and Applications VL - 2 SP - 187 EP - 198 PY - 2018 DA - 2018/07 SN - 34 DO - http://dor.org/10.4208/ata.2018.v34.n2.8 UR - https://global-sci.org/intro/article_detail/ata/12586.html KW - AB -

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.

Bilal A. Chat & S. Pirzada. (1970). On Potentially Graphical Sequences of G−E(H). Analysis in Theory and Applications. 34 (2). 187-198. doi:10.4208/ata.2018.v34.n2.8
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