Some Extremal Problems in (D, D+1)-Regular Graphs

2016 ◽  
Vol 6 (2) ◽  
pp. 105
Author(s):  
N. Murugesan ◽  
R. Anitha
Keyword(s):  
Extremal Problems ◽  
Regular Graphs

scholarly journals Extremal Problems for Independent Set Enumeration

10.37236/656 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Jonathan Cutler ◽  
A. J. Radcliffe
Keyword(s):  
Initial Segment ◽  
Independence Number ◽  
Independent Set ◽  
Independent Sets ◽  
Clique Number ◽  
Extremal Problems ◽  
Fixed Number ◽  
Regular Graphs ◽  
Minimum Number ◽  
Rich History

The study of the number of independent sets in a graph has a rich history. Recently, Kahn proved that disjoint unions of $K_{r,r}$'s have the maximum number of independent sets amongst $r$-regular bipartite graphs. Zhao extended this to all $r$-regular graphs. If we instead restrict the class of graphs to those on a fixed number of vertices and edges, then the Kruskal-Katona theorem implies that the graph with the maximum number of independent sets is the lex graph, where edges form an initial segment of the lexicographic ordering. In this paper, we study three related questions. Firstly, we prove that the lex graph has the maximum number of weighted independent sets for any appropriate weighting. Secondly, we solve the problem of maximizing the number of independents sets in graphs with specified independence number or clique number. Finally, for $m\leq n$, we find the graphs with the minimum number of independent sets for graphs with $n$ vertices and $m$ edges.

Distance-regular graphs which support a spin model are thin

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 205-216 ◽  
Author(s):  
B Curtin
Keyword(s):  
Spin Model ◽  
Regular Graphs ◽  
Distance Regular Graphs

Lower connectivities of regular graphs with small diameter☆

2007 ◽  
Vol 307 (11-12) ◽  
pp. 1255-1265
Author(s):  
C BALBUENA
Keyword(s):  
Small Diameter ◽  
Regular Graphs

Antipodal Krein Graphs and Distance-Regular Graphs Close to Them

2020 ◽  
Vol 101 (3) ◽  
pp. 218-220
Author(s):  
A. A. Makhnev
Keyword(s):  
Regular Graphs ◽  
Distance Regular Graphs

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

Regular graphs of girth 5 from elliptic semiplanes of type C

2021 ◽  
Vol 344 (6) ◽  
pp. 112343
Author(s):  
E. Abajo ◽  
M. Bendala
Keyword(s):  
Regular Graphs ◽  
Type C
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