### Inverse Sum Indeg Coindex of Graphs

#### Abstract

The inverse sum indeg coindex

$\overline{ISI}(G)$ of a simple connected graph $G$ is defined as the

sum of the terms $\frac{d_G(u)d_G(v)}{d_G(u)+d_G(v)}$ over all edges $uv$ not in $G,$ where $d_G(u)$

denotes the degree of a vertex $u$ of $G.$ In this paper, we present the upper

bounds on inverse sum indeg coindex of edge corona product graph and Mycielskian graph. In addition,

we obtain the exact value of both inverse sum indeg index and its coindex of a double graph.

$\overline{ISI}(G)$ of a simple connected graph $G$ is defined as the

sum of the terms $\frac{d_G(u)d_G(v)}{d_G(u)+d_G(v)}$ over all edges $uv$ not in $G,$ where $d_G(u)$

denotes the degree of a vertex $u$ of $G.$ In this paper, we present the upper

bounds on inverse sum indeg coindex of edge corona product graph and Mycielskian graph. In addition,

we obtain the exact value of both inverse sum indeg index and its coindex of a double graph.

#### Keywords

Inverse sum indeg index, edge corona graph, Mycielskian graph, double graph

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