ON GRAPH-BASED NETWORK PARAMETERS AND COMPONENT FACTORS IN NETWORKS

Many physical structures can conveniently be simulated by networks. To study the properties of the network, we use a graph to simulate the network. A graph H is called an F-factor of a graph G, if H is a spanning subgraph of G and every connected component of H is isomorphic to a graph from the graph set F. An F-factor is also referred as a component factor. The graph-based network parameter degree sum of G is defined by sigma(k) (G)=min(X subset of V(G)) {Sigma(x is an element of X) d(G)(x): X is an independent set of k vertices}. In this article, we give the precise degree sum condition for a graph to have {P-2, C-3, P-5, T (3)}-factor and {K-1,K-1, K-1,K-2, ..., K-1,K-k, T (2k + 1)}-factor. We also obtain similar results for {P-2, C-3, P-5, T (3)}-factor avoidable graph and {K-1,K-1, K-1,K-2, ..., K-1,K-k, T (2k + 1)}-factor avoidable graph, respectively.