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Two novel bidimensional coordination polymers, [Co(azbbpy)(4,4'-bipy)0.5(DMF)(NCS)2]·MeOH (1) and [Co(azbbpy)(bpe)0.5(DMF)(NCS)2]·0.25H2O (2), resulted from the assembling of cobalt(II) ions by 1,3-bis(4-pyridyl)azulene, using either 4,4'-bipyridyl or 1,2-bis(4-pyridyl)ethylene as neutral spacers. The cobalt(II) nodes in 1 and 2 act as single-ion magnets (SIMs).

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Four new heterometallic 3d-4f complexes have been obtained using bi-and trinuclear building blocks:1acetoacetyl)pyridine, azbbpy = 1,3-bis(4-pyridyl)azulene, dca − = dicyanamide anion, and oxy-bbz = the dianion of the 4,4′-oxy-bis(benzoic) acid]. 1 and 2 represent the first complexes containing 1,3-bis(4-pyridyl)azulene as a ligand. 1, 3, and 4 are one-dimensional coordination polymers constructed from heterometallic nodes connected by the exo-dentate ligands. Helical chains are assembled in the case of 4. The analysis of the packing diagram for 1 reveals the occurrence of π-π stackinginteractions established between the azulene rings from neighboring chains, which lead to supramolecular layers. The magnetic properties of 3 in the temperature range 1.9-300 K have been investigated.Intra-node ferromagnetic interactions are established between the Cu II and Gd III ions (J = +2.7 cm −

Eccentricity measures the shortest length of the paths from a given vertex v to reach any other vertex w of a connected graph. Computed for every vertex v it transforms the connectivity structure of the graph into a set of values. For a connected region of a digital image it is defined through its neighbourhood graph and the given metric. This transform assigns to each element of a region a value that depends on it's location inside the region and the region's shape. The definition and several properties are given. Presented experimental results verify its robustness against noise, and its increased stability compared to the distance transform. Future work will include using it for shape decomposition, representation, and matching.

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