# Energy Efficient Multicast Communication in Cognitive Radio Wireless Mesh Network
## 4 Proposed Technique
The tree construction then begins from level L. The forwarding nodes from level L1 are chosen for the potential receiving nodes at level L. For example, in Figure 3 at level L = 3, E and F are the potential receiving nodes and nodes at level L = 2, i.e., D and G, are the candidate forwarding nodes. A bipartite graph is created for each node at level L = 1 to choose the forwarding nodes for the potential receiving nodes of level L. For example, in Figure 3, a bipartite graph needs to be constructed for nodes D and G. A graph G(V, \(\underline{\text{\&}}\)) is called a bipartite graph if the set of vertices V can be partitioned into two disjoint sets, S\({}_{1}\) and S\({}_{2}\) with S\({}_{1}\)S\({}_{2}\) = V, and if every edge in \(\underline{\text{\&}}\) connects a vertex from S\({}_{1}\) to S\({}_{2}\). G\({}_{1}\) (S\({}_{1}\), S\({}_{2}\), \(\underline{\text{\&}}\)) is a bipartite graph, where S1 consists of node i and the potential receiving nodes of level L and S2 consist of the available channels at node i. For example, S1 for nodes G and D consist of nodes {G, E, F} and {D, E}, respectively. S1 for node D does not include F because the distance between nodes D and F is greater than RT. S\({}_{2}\) for G and D consists of the respective channels available at each node. An edge (x, y) exists between vertices such that x \(\in\) S\({}_{1}\) and y \(\in\) S\({}_{2}\) if y \(\in\) C\({}_{\text{x}}\), i.e., channel y is in the list of C\({}_{\text{x}}\). Figure 4 shows the bipartite graph for nodes G and D. For G\({}_{1}\) (S\({}_{1}\), S\({}_{2}\), \(\underline{\text{\&}}\)), find the number of edges finishing on each vertex of S\({}_{2}\) which can be said to be the degree of that vertex. Subsequently, find the vertex with the maximum degree that represents the channel with which the forwarding node can cover the maximum possible potential number of receiving nodes. For example, in Figure 4a, the bipartite graph for node G, channel 2 has the maximum degree of 3. Subsequently, the same procedure is repeated for the remaining candidate forwarding nodes. Finally, the node with the maximum degree is chosen as the forwarding node and the corresponding channel is the selected channel. As illustrated in Figure 4, node G has channel 2 which has the maximum degree of 3, and node D has three channels (2, 3 and 5) which have a degree of 2. Since node G has a channel with the maximum degree, it is selected as the forwarding node and it is assigned to channel 2, which ultimately results in the formation of a hyperlink {(G, 2, [E, F]). Alternatively, if node D is selected as the forwarding node, it cannot cover both nodes E and F. Thus, this mechanism results in the formation of a hyperlink that can cover the maximum number of possible potential receiving nodes. The algorithmic form of this mechanism is given in Algorithm 1. Once a channel is assigned to a hyperlink, all nodes whose distance to any of the nodes involved in this hyperlink (either forwarding or receiving node) is less than R\({}_{\text{T}}\) remove this channel from the list of available channels to ensure the constraint mentioned in (4). Next, if all the potential receiving nodes of level L are covered, a search for forwarding nodes in level L1 is performed by following the same procedure. As shown in Figure 3, both potential receiving nodes, E and F, are covered by the selected forwarding  
Figure 2: (**a**) A, B, C, and D are the forwarding nodes; (**b**) A and C are the forwarding nodes. node G. Otherwise, remove the covered nodes from the list of potential receiving nodes and again execute Algorithm 1 repeatedly until all potential receiving nodes are covered. Figure 4: Bipartite graph for nodes G and D. (**a**) A bipartite graph for node G. (**b**) A bipartite graph for node D.  
Figure 3: An Example of a CR-WMN.