%0 Journal Article
%T Supereulerian Indices of Some Classes of Graphs
%A Shengmei Lv
%A Ziyu An
%J Applied Mathematics
%P 357-364
%@ 2152-7393
%D 2025
%I Scientific Research Publishing
%R 10.4236/am.2025.164019
%X Researching Supereulerian index of a graph <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>G</mi>
</math>

 is NP-hard. In this paper, we consider Supereulerian indices of some classes of graphs, Supereulerian index means the minimum integer <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>k</mi>
</math>

 of iterated line graph <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>L</mi>
   <mi>k</mi>
  </msup>
  <mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

 of a graph <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>G</mi>
</math>

 such that <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>L</mi>
   <mi>k</mi>
  </msup>
  <mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

 is Supereulerian. We show that Supereulerian indices of those graphs obtained by replacing every vertex of Petersen graph with <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>n</mi>
</math>

-cycle or a complete graph of order <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>n</mi>
</math>

, or adding <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>n</mi>
</math>

 pendant edges to each vertex of Petersen graph are both 1. Concurrently, we show that Supereulerian indices of partial Generalized Petersen graphs are also 1.
%K Petersen Graph
%K Generalized Petersen Graph
%K Supereulerian Index
%K Iterated Line Graph
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=142284