Distance-regular graphs with intersection array

Distance regular graphs Γ of diameter 3 for which the graphs Γ2 and Γ3 are strongly regular, studied by M.S. Nirova. For Q-polynomial graphs with intersection arrays (69; 56; 10; 1; 14; 60) and (119; 100; 15; 1; 20; 105} the graph Γ3 is strongly regular and does not contain triangles. Automorphisms of graphs with these intersection arrays were found by A.A. Makhnev, M.S. Nirova and M.M. Isakova, A.A. Makhnev, respectively. The graph Γ with the intersection array (74; 54; 15; 1; 9; 60) also is Q-polynomial, and Γ3 is a strongly regular graph with parameters (630; 111; 12; 21). It is proved in the paper that graphs with intersection arrays (69; 56; 10; 1; 14; 60), (74; 54; 15; 1; 9; 60) and (119; 100; 15; 1; 20; 105) do not exist. © 2019 Sobolev Institute of Mathematics

Pastoralism and Emergent Complex Settlement in the Middle Bronze Age, Azerbaijan: Isotopic analyses of mobility strategies in transformation

Objectives. This article explores the scale and seasonal patterns of mobility at the complex settlement site of Qızqala during the Middle Bronze Age (2400–1,500 BCE). By integrating human bone, teeth, and environmental samples this research tests the hypothesis of the persistent importance of community-wide seasonal pastoral transhumance during the early formation of complex settlement systems of the South Caucasus. Methods. This research applies stable oxygen and radiogenic strontium isotope analyses on incremental samples of human tooth enamel, bulk tooth enamel, and bone to resolve mobility patterns. Sequential and bulk sampling techniques elucidate seasonal and residential mobility behaviors. Extensive environmental isotope samples of plant and water were collected through regional survey and establish local and regional isotopic baselines, which are compared to human isotope analysis results. Results. Qızqala individuals exhibit low isotopic variability compared to regional contemporaries. 87Sr/86Sr ratios from human remains indicate seasonal and residential isotopic variability within the baseline ranges of local landscapes. δ18O values display erratic patterns, but correspond to seasonal variability with fluctuations between highland and lowland altitudinal zone baseline values. Conclusions. Results suggest that isotopic analysis of multiple elements and sequential enamel samples offers finer resolution on the complexities of human mobility strategies and elucidate the daily lives of often overlooked mobile populations. Higher resolution of individual mobility reveals shared routine behaviors that underscore the importance of diverse social collaborations in forming complex polities in the South Caucasus

О дистанционно–регулярных графах с = 2

V.P.Burichenko and A.A.Makhnev have found intersection arrays of distance-regular graphs with = 2, μ > 1, having at most 1000 vertices. Earlier, intersection arrays of antipodal distance-regular graphs of diameter 3 with 6 2 and μ = 1 were obtained by the second author. In this paper, the possible intersection arrays of distance-regular graphs with = 2 and the number of vertices not greater than 4096 are obtainedВ.П.Буриченко и А.А.Махнев нашли массивы пересечений дистанционно регулярных графов с = 2, μ > 1 и числом вершин не большим 1000. Ранее вторым автором найдены массивы пере- сечений антиподальных дистанционно-регулярных графов диаметра 3 с 6 2 и μ = 1. В данной статье найдены возможные массивы пересечений дистанционно-регулярных графов с = 2 и не более 4096 вершинам

О дистанционно–регулярных графах с = 2

V.P.Burichenko and A.A.Makhnev have found intersection arrays of distance-regular graphs with = 2, μ > 1, having at most 1000 vertices. Earlier, intersection arrays of antipodal distance-regular graphs of diameter 3 with 6 2 and μ = 1 were obtained by the second author. In this paper, the possible intersection arrays of distance-regular graphs with = 2 and the number of vertices not greater than 4096 are obtainedВ.П.Буриченко и А.А.Махнев нашли массивы пересечений дистанционно регулярных графов с = 2, μ > 1 и числом вершин не большим 1000. Ранее вторым автором найдены массивы пере- сечений антиподальных дистанционно-регулярных графов диаметра 3 с 6 2 и μ = 1. В данной статье найдены возможные массивы пересечений дистанционно-регулярных графов с = 2 и не более 4096 вершинам