  Providing an analytical solution for the problem of finding Fastest
Distributed Consensus (FDC) is one of the challenging problems in the field of
sensor networks. Here in this work we present analytical solution for the
problem of fastest distributed consensus averaging algorithm by means of
stratification and semi-definite programming, for two particular types of Petal
networks, namely symmetric and Complete Cored Symmetric (CCS) Petal networks.
Our method in this paper is based on convexity of fastest distributed consensus
averaging problem, and inductive comparing of the characteristic polynomials
initiated by slackness conditions in order to find the optimal weights. Also
certain types of leaves are introduced along with their optimal weights which
are not achievable by the method used in this work if these leaves are
considered individually.
