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Diameter of a special type of regular graph of degree 4 whose order maintain an increase in form of an arithmetic progression.
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%I #9 Apr 11 2024 10:04:21

%S 1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,

%T 10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,15,15,

%U 15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,20,20,21,21,21

%N Diameter of a special type of regular graph of degree 4 whose order maintain an increase in form of an arithmetic progression.

%D Claude C.S. and Dinneen M.J (1998), Group-theoretic methods for designing networks, Discrete mathematics and theoretical computer science, Research report

%D Comellas, F. and Gomez, J. (1995), New large graphs with given degree and diameter, in Proceedings of the seventh quadrennial international conference on the theory and applications of graphs, Volume 1: pp. 222-233

%D Ibrahim, A., A. (2007), A stable variety of Cayley graphs (in preparation)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphThickness.html">Graph Thickness</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1).

%F f(D4,5)=1: Order =4,5; f(D)= f(D4,5)+n: order=5+n, n=1,2,...

%F I am assuming this sequence is just Floor[(n+5)/4]... [From _Eric W. Weisstein_, Sep 09 2008]

%e f(D4,5)=1 when order=4, f(D4,5)=1 when order=5, f(D)=f(D4,5)+1=1+1=2 when order is 5+1=6

%Y Cf. A123642.

%Y First differences of A186347.

%K nonn

%O 4,3

%A _Aminu Alhaji Ibrahim_, Apr 25 2007