Abstract
Recently we introduced the concept of minimum dominating energy[21]. Motivatedby this paper,we introduced the concept of minimum dominating distance energyEDd(G) of a graph G and computed minimum dominating distance energies of a Stargraph,Complete graph,Crown graph and Cocktail graphs. Upper and lower boundsfor EDd(G) are also established.DOI : http://dx.doi.org/10.22342/jims.20.1.133.19-29
Highlights
The concept of energy of a graph was introduced by I
The minimum dominating distance matrix of G is the n × n matrix defined by ADd(G) :=, where dij =
For any integer n ≥ 3, the minimum dominating distance energy of star graph K1,n−1 is equal to 4n − 7
Summary
The concept of energy of a graph was introduced by I. Let G be a graph with n vertices {v1, v2, ..., vn} and m edges. Let A = (aij ) be the adjacency matrix of the graph. The energy E(G) of G is defined to be the sum of the absolute values of the eigenvalues of G. i.e., n. For details on the mathematical aspects of the theory of graph energy see the reviews[10], paper [11] and the references cited there in. Let ρ1, ρ2, ..., ρn be the eigenvalues of the distance matrix of G. The distance energy DE is defined by n. Detailed studies on distance energy can be found in [3, 4, 8, 13, 14, 22]
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