On the forgotten topological index of signed graphs - Pirzada, Shariefuddin; Rashid, Mir Riyaz Ul (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 519.17The forgotten topological index denoted by $F(G)$ of a graph $G=(V,E)$ is defined as follows: $F(G)=\displaystyle\sum olimits_{i=1}^{n}\!d_v^3,$ 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 $Σ_1=(G_1,σ_1)$ and $Σ_2=(G_2,σ_2),$ along with their sizes and orders.