Kirchhoff index of composite graphs

AbstractLet G1+G2, G1∘G2 and G1{G2} be the join, corona and cluster of graphs G1 and G2, respectively. In this paper, Kirchhoff index formulae of these composite graphs are given

Relations Between Resistance Distances of a Graph and its Complement or its Contraction

The resistance distance between two vertices of a connected graph is defined as the net effective resistance between them when each edge of the graph is replaced by a resistor. In this paper, it is shown that the product of resistance distances between any pair of vertices in a simple graph and in its connected complement is less than or equal to 3. Meanwhile, a relation between resistance distances of a graph and its contraction is obtained in a special case. (doi: 10.5562/cca2318