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## Discrete Mathematics and its Applications based on Trees

Primary objective of this lecture is to analysis Discrete Mathematics and its Applications based on Trees. A tree is often a connected undirected graph without any simple circuits. Brief hypothesis: An undirected graph is often a tree if and only if there is a unique simple way between any two associated with its vertices. Here briefly explain Internal Vertex and Binary Tree. Here also analysis on Ancestors: The ancestors of a non-root vertex are all the vertices in the path from root to this vertex and Descendants: The descendants of vertex v are all the vertices that have v as an ancestor. Finally discuss Traversal Algorithms with examples.

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## Data Gathering Tree for Wireless Sensor Networks

This lecture focus to explain Bottleneck Node Avoidance Data Gathering Tree forWireless Sensor Networks. Here briefly explain Wireless Sensor Network (WSNs), Energy Problem in WSNs, Data Gathering Methodology and Data Gathering Tree (DG), Energy Aware Maximum Leaf node DG (EML-DG), Proposed Energy Aware Bottleneck Avoidance Shortest Path DG etc. Finally discuss on some advantages of Wireless Sensor Networks, like: decrease the total energy lost per round, decrease path cost, increase average lifetime of the bottlenecks, decrease height of the tree and increase the lifetime of the network.