REST OF A VERTEX IN A GRAPH
R. Rajendra, Polaepalli Siva Kota Reddy, C. N. Harshavardhana · Advances in Mathematics Scientific Journal · 2021
We define the rest of a vertex $v$ in a graph as the number of geodesics passing through $v$ minus the degree of $v$. The total rest of a graph is the sum of rests of all the vertices in that graph. We made some observations, compute rest of vertices in some standard graphs and obtain some interesting results.