For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling $\phi :E\left(G\right)\to \{1,2,\dots ,k\}$ of positive integers to the edges of G is called irregular if the weights of the vertices, defined as $w{t}_{\phi }\left(v\right)={\sum }_{u\in N\left(v\right)}\phi \left(uv\right)$, are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to ∞ if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs.

In mathematical models, for forecasting prices on commodity exchanges different mathematical methods are used. In the given paper the numerical model based on the exponential approximation of commodity stock exchanges was derived. The price pr...

Let H be a graph. A graph G=(V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called (a,d)-H-antimagic if there is a bij...