Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let R ( G ) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge. Let I ( G ) be the set of newly added vertices. The R-vertex corona of G1 and G2, denoted by G 1 ? G 2 , is the graph obtained from vertex disjoint R ( G 1 ) and | V ( G 1 ) | copies of G2 by joining the ith vertex of V ( G 1 ) to every vertex in the ith copy of G2. The R-edge corona of G1 and G2, denoted by G 1 ? G 2 , is the graph obtained from vertex disjoint R ( G 1 ) and | I ( G 1 ) | copies of G2 by joining the ith vertex of I ( G 1 ) to every vertex in the ith copy of G2. Liu et al. gave formulae for the Laplacian polynomial and Kirchhoff index of RT ( G ) in 19. ,  give the Laplacian polynomials of G 1 ? G 2 and G 1 ? G 2 for a regular graph G1 and an arbitrary graph G2; on the other hand,  derive formulae and lor bounds of Kirchhoff index of these graphs and generalize the existing results.
['Qun Liu', 'Jia-Bao Liu', 'Jinde Cao']
I am writing a research paper on a idea The Laplacian polynomial and Kirchhoff index of graphs based on R-graphs
[{"from": "human", "value": "I am writing a research paper on a idea The Laplacian polynomial and Kirchhoff index of graphs based on R-graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let R ( G ) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge. Let I ( G ) be the set of newly added vertices. The R-vertex corona of G1 and G2, denoted by G 1 ? G 2 , is the graph obtained from vertex disjoint R ( G 1 ) and | V ( G 1 ) | copies of G2 by joining the ith vertex of V ( G 1 ) to every vertex in the ith copy of G2. The R-edge corona of G1 and G2, denoted by G 1 ? G 2 , is the graph obtained from vertex disjoint R ( G 1 ) and | I ( G 1 ) | copies of G2 by joining the ith vertex of I ( G 1 ) to every vertex in the ith copy of G2. Liu et al. gave formulae for the Laplacian polynomial and Kirchhoff index of RT ( G ) in 19. ,  give the Laplacian polynomials of G 1 ? G 2 and G 1 ? G 2 for a regular graph G1 and an arbitrary graph G2; on the other hand,  derive formulae and lor bounds of Kirchhoff index of these graphs and generalize the existing results."}]