The term "irregular graph" may be used to refer to a graph that is not
regular.
However, a different definition considers an edge-weighted graph in which each edge is assigned a positive integer weight and the degree of a vertex is defined as the
sum of the weights of its incident edges. Such a graph may be termed irregular if
all the vertices have distinct degrees (Faudree et al. 1989, Przybylo 2024).
Chartrand, G.; Erdős, P.; and Oellermann, O. R. "How to Define an Irregular Graph." College Math. J.19,
36-42, 1988.Faudree, R.; Schelp, R.; Jacobson, M.; and Lehel, J. "Irregular
Networks, Regular Graphs and Integer Matrices With Distinct Row and Column Sums."
Disc. Math.76,) 223-240, 1989.Przybylo, J. "The
Irregularity Strength of Dense Graphs--On Asymptotically Optimal Solutions of Problems
of Faudree, Jacobson, Kinch and Lehel." 13 Jun 2024. https://arxiv.org/abs/2406.09584.
