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 ₖ (G) =X V (G) \, \{x X{\, dG (x): Xis an independent set ofkvertices\}. } 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, 1, K 1, 2, …, K 1, k, T (2 k + 1) -factor. We also obtain similar results for P 2, C 3, P 5, T (3) -factor avoidable graph and K 1, 1, K 1, 2, …, K 1, k, T (2 k + 1) -factor avoidable graph, respectively.