<abstract xmlns="http://www.w3.org/1999/xhtml"> An r-graph(or a multigraph) is a loopless graph in which no two vertices are joined by more than r edges. An r-complete graph on n vertices, denoted by Kn(r) , is an r-graph on n vertices in which each pair of vertices is joined by exactly r edges. A non-increasing sequence π = (d1, d2, ..., dn) of non-negative integers is said to be r-graphic if it is realizable by an r-graph on n vertices. An r-graphic sequence π is said to be potentially SL;M(r) -graphic if it has a realization containing SL;M(r) as a subgraph. We obtain conditions for an r-graphic sequence to be potentially S(r) L;M-graphic. These are generalizations from split graphs to p-tuple r-split graph. </abstract>

An r-graph(or a multigraph) is a loopless graph in which no two vertices are joined by more than r edges. An r-complete graph on n vertices, denoted by Kn(r) , is an r-graph on n vertices in which each pair of vertices is joined by exactly r edges. A non-increasing sequence π = (d1, d2, ..., dn) of non-negative integers is said to be r-graphic if it is realizable by an r-graph on n vertices. An r-graphic sequence π is said to be potentially SL;M(r) -graphic if it has a realization containing SL;M(r) as a subgraph. We obtain conditions for an r-graphic sequence to be potentially S(r) L;M-graphic. These are generalizations from split graphs to p-tuple r-split graph.

On multigraphic and potentially multigraphic sequences

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Dedicated to the memory of Antal Iványi

An r-graph(or a multigraph) is a loopless graph in which no two vertices are joined by more than r edges. An r-complete graph on n vertices, denoted by Kn(r) ,...

On multigraphic and potentially multigraphic sequences

Published Online: Aug 01, 2017

Page range: 35 - 47

Received: Nov 30, 2016

DOI: https://doi.org/10.1515/ausi-2017-0003

Keywords
multigraph, multigraphic sequence, potentially multigraphic sequences, split graph

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On multigraphic and potentially multigraphic sequences

Published Online: Aug 01, 2017

Page range: 35 - 47

Received: Nov 30, 2016

DOI: https://doi.org/10.1515/ausi-2017-0003

Keywordsmultigraph, multigraphic sequence, potentially multigraphic sequences, split graph

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
multigraph, multigraphic sequence, potentially multigraphic sequences, split graph