On the forgotten topological index of signed graphs
Abstract
UDC 519.17 The forgotten topological index denoted by $F(G)$ of a graph $G=(V,E)$ is defined as follows: $F(G)=\displaystyle\sum\nolimits_{i=1}^{n}\!d_v^3,$ where $d_v$ denotes the degree of the vertex $v.$ We extend the notion of forgotten topological index to signed graphs and introduce the $MS$-index of a signed graph. Moreover, we determine the forgotten topological index for the tensor product, Cartesian product, lexicographic product, strong product, symmetric difference, and the joint of the graphs $G_1$ and $G_2$ in terms of the forgotten topological index, the first Zagreb index, and the $M\kern-1ptS$-index of signed graphs $\Sigma_1=(G_1,\sigma_1)$ and $\Sigma_2=(G_2,\sigma_2),$ along with their sizes and orders.
Fields of Study & Subjects
Graph theory and applications
Graph Labeling and Dimension Problems
Graph Theory and Algorithms
Publication details
- Journal / source
- Ukrains’kyi Matematychnyi Zhurnal
- Volume
- 78
- Issue
- 1-2
- Pages
- 89–90
- Publication date
- 27 January 2026
- Language
- EN