<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The eigenvalues of the adjacency matrix of a graph form the spectrum of the graph. The multiplicity of the eigenvalue zero in the spectrum of a graph is called nullity of the graph. Fan and Qian (2009) obtained the nullity set of <italic>n</italic>-vertex bipartite graphs and characterized the bipartite graphs with nullity <italic>n</italic> − 4 and the regular <italic>n</italic>-vertex bipartite graphs with nullity <italic>n</italic> − 6. In this paper, we study similar problem for a class of tripartite graphs. As observed the nullity problem in tripartite graphs does not follow as an extension to that of the nullity of bipartite graphs, this makes the study of nullity in tripartite graphs interesting. In this direction, we obtain the nullity set of a class of <italic>n</italic>-vertex tripartite graphs and characterize these tripartite graphs with nullity <italic>n</italic> − 4. We also characterize some tripartite graphs with nullity <italic>n</italic> − 6 in this class.</p></abstract>

The eigenvalues of the adjacency matrix of a graph form the spectrum of the graph. The multiplicity of the eigenvalue zero in the spectrum of a graph is called nullity of the graph. Fan and Qian (2009) obtained the nullity set of n-vertex bipartite graphs and characterized the bipartite graphs with nullity n − 4 and the regular n-vertex bipartite graphs with nullity n − 6. In this paper, we study similar problem for a class of tripartite graphs. As observed the nullity problem in tripartite graphs does not follow as an extension to that of the nullity of bipartite graphs, this makes the study of nullity in tripartite graphs interesting. In this direction, we obtain the nullity set of a class of n-vertex tripartite graphs and characterize these tripartite graphs with nullity n − 4. We also characterize some tripartite graphs with nullity n − 6 in this class.

On the nullity of a family of tripartite graphs

School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the nullity of a family of tripartite graphs"}

The eigenvalues of the adjacency matrix of a graph form the spectrum of the graph. The multiplicity of the eigenvalue zero in the spectrum of a graph is called...

On the nullity of a family of tripartite graphs

Published Online: Jun 20, 2016

Page range: 96 - 107

Received: Apr 12, 2016

DOI: https://doi.org/10.1515/ausi-2016-0006

Keywords
nullity, tripartite graph, expanded path

© 2016 Rashid Farooq et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the nullity of a family of tripartite graphs

Published Online: Jun 20, 2016

Page range: 96 - 107

Received: Apr 12, 2016

DOI: https://doi.org/10.1515/ausi-2016-0006

Keywordsnullity, tripartite graph, expanded path

© 2016 Rashid Farooq et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nullity, tripartite graph, expanded path