On edge-girth-regular graphs: lower bounds and new familiesPorupsánszki, István (Avtor) cage problemextremal graph theorygeneralized polygonsovoidsAn edge-girth-regular graph egr(n, k, g, λ) is a k-regular graph of order n, girth g and with the property that each of its edges is contained in exactly λ distinct g-cycles. We present new families of edge-girth regular graphs arising from generalized quadrangles and pencils of elliptic quadrics. An egr(n, k, g, λ) is called extremal for the triple (k, g, λ) if n is the smallest order of any egr(n, k, g, λ). We give new lower bounds for the order of extremal edge-girth-regular graphs using properties of the eigenvalues of the adjacency matrix of a graph.Založba Univerze na Primorskem20252025-10-22 22:16:21Članek v reviji22020UDK: 519.17eISSN: 1855-3974DOI: https://doi.org/10.26493/1855-3974.3107.9dfsl