| Summary: | An antimagic labeling of a graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></semantics></math></inline-formula> is a bijection from the set of edges of <i>G</i> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="{" close="}"><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mfenced separators="" open="|" close="|"><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo></mfenced></mfenced></semantics></math></inline-formula> and such that any two vertices of <i>G</i> have distinct vertex sums where the vertex sum of a vertex <i>v</i> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> is nothing but the sum of all the incident edge labeling of <i>G</i>. In this paper, we discussed the antimagicness of rooted product and corona product of graphs. We proved that if we let <i>G</i> be a connected <i>t</i>-regular graph and <i>H</i> be a connected <i>k</i>-regular graph, then the rooted product of graph <i>G</i> and <i>H</i> admits antimagic labeling if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>≥</mo><mi>k</mi></mrow></semantics></math></inline-formula>. Moreover, we proved that if we let <i>G</i> be a connected <i>t</i>-regular graph and <i>H</i> be a connected <i>k</i>-regular graph, then the corona product of graph <i>G</i> and <i>H</i> admits antimagic labeling for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>,</mo><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>.
|
|---|