A function on graphs (Q1594148)

An undirected graph \(G\) is considered which may contain loops and multiple edges. A subgraph \(\Gamma\) of \(G\) is called admissible, if it contains all vertices of \(G\) and each vertex in \(\Gamma\) has an odd degree. By means of the set of admissible subgraphs of \(G\), the so-called Ivanovskij function \(f(x)\) is defined. The main theorem says that always \(f(x)\equiv 0\pmod {2^b}\), where \(b=r+s-n\), here \(r,s,n\) are the number of edges, connected components and vertices of \(G\), respectively. It seems to the reviewer that the author neglected exactness in the notation and thus the paper is not quite intelligible.