Entanglement of graph states of spin system with Ising interaction and its quantifying on IBM's quantum computer

•Graph states generated by operator of evolution with Ising Hamiltonian are examined.•Entanglement of a spin with other spins in graph state is found on quantum computer.•The results of quantum calculations are in good agreement with the theoretical ones.•Entanglement of graph states is related with properties of the corresponding graphs. We consider graph states generated by operator of evolution with Ising Hamiltonian. The geometric measure of entanglement of a spin with other spins in the graph state is obtained analytically and quantified on IBM's quantum computer, IBM Q Valencia. The results of quantum calculations are in good agreement with the theoretical ones. We conclude that the geometric measure of entanglement of a spin with other spins in the graph state is related with degree of vertex representing the spin in the corresponding graph.