On graph-based network parameters and component factors in networks

¹ School of Management & Engineering, Nanjing University, Nanjing 210093, P.R. China
² College of Science, Nanjing Forestry University, Nanjing, Jiangsu 210037, P.R. China
³ School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210023, P.R. China
⁴ School of Mathematics, University of Birmingham, B15 2TT, UK

^* Corresponding author: daiguowei@njfu.edu.cn

Received: 12 February 2024
Accepted: 23 June 2024

Abstract

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

In this article, we give the precise degree sum condition for a graph to have {P₂, C₃, P₅, T (3)}-factor and {K_1,1, K_1,2, …, K_1,k, T (2k + 1)}-factor. We also obtain similar results for {P₂, C₃, P₅, T (3)}-factor avoidable graph and {K_1,1, K_1,2, …, K_1,k, T (2k + 1)}-factor avoidable graph, respectively.