OFFSET
1,1
COMMENTS
The sigma irregularity of a graph is the sum of the squares of the differences between the degrees over all edges of the graph.
LINKS
Allan Bickle and Zhongyuan Che, Irregularities of Maximal k-degenerate Graphs, Discrete Applied Math. 331 (2023) 70-87.
Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (n^4 + 2*n^3 + 2*n^2 + n)/3.
a(n) = 2*A006325(n+1).
G.f.: 2*x*(1 + x)^2/(1 - x)^5. - Stefano Spezia, Jul 28 2023
EXAMPLE
A path of length at least 3 has two edges between vertices with degrees 1 and 2. Thus a(1) = 2.
MATHEMATICA
Table[(n^4 + 2*n^3 + 2*n^2 + n)/3, {n, 1, 40}] (* Amiram Eldar, Jul 28 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Allan Bickle, Jun 16 2023
STATUS
approved