Double domination number of inflated graphs

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<p>In a graph, a vertex is said to dominate itself and all its neighbors. A subset <span class="math inline">\(S\subseteq V(G)\)</span> is a double dominating set of a graph <span class="math inline">\(G\)</span>, if every vertex of <span class="math inline">\(V\)</span> is dominated by at least two vertices of <span class="math inline">\(S\)</span>. The double domination number denoted by <span class="math inline">\(\gamma_{2\times(G)}\)</span> is the minimum cardinality of a double dominating set. Graph operations are fundamental in graph theory and have various applications across different fields including network analysis, parallel computing and electrical circuit design. This paper studies the problem of finding the double domination number under unary and binary operations of graphs. We investigate the double domination number of graphs under unary operations such as inflation and cubic inflation. Also, we introduced two new unary operations inspired from inflation operation and studied the impact of these operations on double domination number. Further, we explore the double domination number of edge corona and neighborhood corona of two graphs. Additionally, we study the double domination number of various corona operations of two graphs combined with subdivision of a graph and <span class="math inline">\(R-\)</span>graph.</p>