In this study, from a tree with a quasi-spanning face, the algorithm will route Hamiltonian cycles. Goodey pioneered the idea of holding facing 4 to 6 sides of a graph concurrently. Similarly, in the three connected cubic planar graphs with two-colored faces, the vertex is incident to one blue and two red faces. As a result, all red-colored faces must gain 4 to 6 sides, while all obscure-colored faces must consume 3 to 5 sides. The proposed routing approach reduces the constriction of all vertex colors and the suitable quasi-spanning tree of faces. The presented algorithm demonstrates that the spanning tree parity will determine the arbitrary face based on an even degree. As a result, when the Lemmas 1 and 2 theorems are compared, the greedy routing method of Hamiltonian cycle faces generates valuable output from a quasi-spanning tree. In graph idea, a dominating set for a graph
S
=
V
,
E
is a subset
D
of
V
. The range of vertices in the smallest dominating set for
S
is the domination number (
S
). Vizing’s conjecture from 1968 proves that the Cartesian fabricated from graphs domination variety is at least as big as their domination numbers production. Proceeding this work, the Vizing’s conjecture states that for each pair of graphs
S
,
L
.
Cloud computing is a revolutionary computing paradigm, which enables flexible, on-demand, and low-cost usage of computing resources, but the data is outsourced to some cloud servers, and various privacy concerns emerge from it. Various schemes based on the attribute-based encryption have been to secure the cloud storage. Data content privacy. A semi anonymous privilege control scheme AnonyControl to address not only the data privacy. But also the user identity privacy. AnonyControl decentralizes the central authority to limit the identity leakage and thus achieves semi anonymity. The Anonymity –F which fully prevent the identity leakage and achieve the full anonymity.
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