With the dynamic and mobile nature of ad hoc networks, links may fail due to topology changes. So, a major challenge in ad hoc network is dynamically to search paths from a source to destination with an efficient routing method, which is an important issue for delay-sensitive real-time application. The main concerns of graph theory in communications are finding connectivity and searching paths using given nodes. A topology of the nodes in ad hoc networks can be modeled as an adjacency matrix.In this paper, based on this adjacency matrix, we propose new path search algorithms using a sequence of matrix calculation. The proposed algorithms can search paths from a destination to a source using connectivity matrix. Two matrix-based algorithms for two different purposes are proposed. Matrix-Based Backward Path Search(MBBS) algorithm is designed for shortest path discovery and Matrix-Based Backward Multipath Search(MBBMS) algorithm is for multipath search. (a) 0 0 0 2 2 2 1 1 0

MANET(Mobile Ad hoc Network) is a collection of two or more nodes equipped with wireless communications and constrained by the factor of energy limitation. The running out of energy on some nodes may bring down the performance of network seriously. For solving the problems above, this paper uses completely separated Node-Disjoint multipaths from a source to a destination as many as possible.And, based on average, minimum or variance of energy values on the each multipath, the packets are distributed on paths. Generally, collecting methods for energy information can be classified into two main categories, Static and Dynamic. As the different energy values collected, the packet distribution methods are classified into six criteria, Static-Average, Static-Minimum, Static-Variance, Dynamic-Average, Dynamic-Minimum and Dynamic-Variance respectively. The performance of the packet distribution methods and that of AODV are compared by NS2 simulation.