Abstract A $$2-(v, k, \lambda )$$ 2 - ( v , k , λ ) design is additive if, up to isomorphism, the point set is a subset of an abelian group G and every block is zero-sum. This definition was introduced in Caggegi et al. (J Algebr Comb 45:271-294, 2017) and was the starting point of an interesting new theory. Although many additive designs have been constructed and known designs have been shown to be additive, these structures seem quite hard to construct in general, particularly when we look for additive Steiner 2-designs. One might generalize additive Steiner 2-designs in a natural way to graph decompositions as follows: given a simple graph $$\Gamma $$ Γ , an additive $$(K_v,\Gamma )$$ ( K v , Γ ) -design is a decomposition of the graph $$K_v$$ K v into subgraphs ( blocks ) $$B_1,\dots ,B_t$$ B 1 , ⋯ , B t all isomorphic to $$\Gamma $$ Γ , such that the vertex set $$V(K_v)$$ V ( K v ) is a subset of an abelian group G , and the sets $$V(B_1), \dots , V(B_t)$$ V ( B 1 ) , ⋯ , V ( B t ) are zero-sum in G . In this work we begin the study of additive $$(K_v,\Gamma )$$ ( K v , Γ ) -designs: we develop different tools instrumental in constructing these structures, and apply them to obtain some infinite classes of designs and many sporadic examples. We will consider decompositions into various graphs $$\Gamma $$ Γ , for instance cycles, paths, and k -matchings. Similar ideas will also allow us to present here a sporadic additive 2-(124, 4, 1) design.

Abstract A 2- $$(v,k,\lambda )$$ ( v , k , λ ) design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG $$_d(n,q)$$ d ( n , q ) , which was known to be additive only for $$q=2$$ q = 2 or $$d=n-1$$ d = n - 1 , is always established.

Today it is already widely accepted that out of school education exceeds formal education in content and knowledge and that it is not a plus, but a necessity. However, unlike formal education, educators working in informal settings are often volunteers or/and they do those activities on top of their daily jobs. The research questions we pose here are (i) what motivates people to volunteer in K-12 Science, Technology, Engineering, Mathematics and Computer Science (STEM-C) informal education, (ii) what could help to motivate people who are currently demotivated, and finally (iii) what we can do not only to attract new volunteers, but also to retain the current ones. We collected and analyzed opinions of faculty staff, students and volunteers involved in K-12 STEM-C outreach activities conducted at University of Zagreb Faculty of Electrical Engineering and Computing, Croatia where five years ago, we started our outreach program named SUZA - From school to science and the academic community. The results of our research study show a wide span of reasons why (and why not) people volunteer in our activities, together with their general attitudes toward K-12 STEM-C outreach activities. Although the results are mostly in line with research in the field, there are some specifics which could relate to specifics of volunteering in K-12 STEM-C fields and could benefit wider community.