We initiate the study of what we refer to as random walk labelings graphs. These are graph that obtainable by performing a on graph, such labeling occurs increasingly whenever an unlabeled vertex is encountered. Some results obtain involve sums inverses binomial coefficients, for which new identities. In particular, prove ∑k = 0n − 12k(2k+1)−1 (binom(2k)(k))-1 (binom(n+k)(k)) (binom(2n)(n)) 12k...

Recently graph auto-encoders have received increasingly widespread attention as one of the important models in field deep learning. Existing auto-encoder only use convolutional neural networks (GCNs) encoders to learn embedding representation nodes. However, GCNs are suitable for transductive learning, poor scalability and shallow with a perceptual field, limitations node feature extraction. To...

In this paper, we analyze the secure connectivity in Shotgun cellular systems (SCS: Wireless communication systems with randomly placed base stations) by Poisson intrinsically secure communication graph (IS-graph), i.e., a random graph which describes the connections that are secure over a network. For a base-station in SCS, a degree of secure connections is determined over two channel models: ...