The Gutman Index of the Unicyclic Graphs with pendent edges

Abstract

Abstract The graph-parameters mainly studies vertex degree and distance between unordered vertices. There are many graph-parameters, and this paper mainly focuses on the Gutman index. For the sake of discussion, this paper puts forward the concept of “contribution” based on the relationship between Gutman index of graph and vertex-Gutman index. On this basis, we discussed the Gutman index of unicyclic graph with pendent edges in odd and even parts, and gave the corresponding extremal graphs, which lays a foundation for the study of the Gutman index of other cycle graphs.