Resistance distance and Kirchhoff index in generalized R-vertex and R-edge corona for graphs

2018/10/08 by Liu, Qun
#Combinatorics (math.CO) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1810.03327

Abstract

For a graph G, the graph R(G) of a graph G is the graph obtained by adding a new vertex for each edge of G and joining each new vertex to both end vertices of the correspond- ing edge. Let I(G) be the set of newly added vertices. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of generalized R-vertex and R-edge corona whenever G and Hi are arbitrary graph. These results generalize the existing results in [9].

Related

• Resistance distance and Kirchhoff index in the corona-vertex and the corona - edge of subdivision graph
• The resistance distance and Kirchhoff index on quadrilateral graph and pentagonal graph
• Resistance distance and Kirchhoff index in central vertex join and central edge join of two graphs
• Resistance distance-based graph invariants of subdivisions and triangulations of graphs
• Results on resistance distance and Kirchhoff index of graphs with generalized pockets