scholarly journals A class of amply regular graphs related to the subconstituents of a dual polar graph

2006 ◽  
Vol 306 (22) ◽  
pp. 2909-2915 ◽  
Author(s):  
Feng-Gao Li ◽  
Yang-Xian Wang
Keyword(s):  
Regular Graphs ◽  
Polar Graph ◽  
Dual Polar Graph

scholarly journals The Smallest Strictly Neumaier Graph and its Generalisations

10.37236/8189 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Rhys J. Evans ◽  
Sergey Goryainov ◽  
Dmitry Panasenko
Keyword(s):  
Positive Integer ◽  
Regular Graph ◽  
Regular Graphs ◽  
Current Interest ◽  
Polar Graph ◽  
Strongly Regular ◽  
Regular Cliques

A regular clique in a regular graph is a clique such that every vertex outside of the clique is adjacent to the same positive number of vertices inside the clique. We continue the study of regular cliques in edge-regular graphs initiated by A. Neumaier in the 1980s and attracting current interest. We thus define a Neumaier graph to be an non-complete edge-regular graph containing a regular clique, and a strictly Neumaier graph to be a non-strongly regular Neumaier graph. We first prove some general results on Neumaier graphs and their feasible parameter tuples. We then apply these results to determine the smallest strictly Neumaier graph, which has $16$ vertices. Next we find the parameter tuples for all strictly Neumaier graphs having at most $24$ vertices. Finally, we give two sequences of graphs, each with $i^{th}$ element a strictly Neumaier graph containing a $2^{i}$-regular clique (where $i$ is a positive integer) and having parameters of an affine polar graph as an edge-regular graph. This answers questions recently posed by G. Greaves and J. Koolen.

scholarly journals Remarks on the energy of regular graphs

2016 ◽  
Vol 508 ◽  
pp. 133-145 ◽  
Author(s):  
V. Nikiforov
Keyword(s):  
Regular Graphs

scholarly journals The cyclic matching sequenceability of regular graphs

2021 ◽  
Author(s):  
Daniel Horsley ◽  
Adam Mammoliti
Keyword(s):  
Regular Graphs
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