Abstract
Randić energy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randić energy REC (G) of a graph G in this paper. This paper contains computation of minimum covering Randić energies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randić energy are also presented.
Highlights
Study on energy of graphs goes back to the year 1978, when I
We have introduced the minimum covering Randić energy REC (G) of a graph G in this paper
( ) minimum covering Randić matrix of G is the n × n matrix defined by RC (G) := rij, where rij 1 di d j if viv j
Summary
Study on energy of graphs goes back to the year 1978, when I. All graphs considered in this paper are assumed to be simple without loops and multiple ( ) edges. Let A = aij be the adjacency matrix of the graph G with its eigenvalues λ1. The sum of the absolute eigenvalues values of G is called the energy E (G) of G. i.e.,. Theories on the mathematical concepts of graph energy can be seen in the reviews[3], papers [4] [5] [6] and the references cited there in. For various upper and lower bounds for energy of a graph can be found in papers[7] [8] and it was observed that graph energy has chemical applications in the molecular orbital theory of conjugated mo-. Jagadeesh lecules [9] [10]
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