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This paper established the idea of minimum evdominating matrix of semigraph and calculated its energy. The minimum ev-dominating energy EmeD(G) of a semigraph G is the sum of the absolute values of the eigenvalues of the minimum ev-dominating matrix. Here some results are also derived in connection with the energy of minimum evdominating matrix. Some lower bounds are also established. [ABSTRACT FROM AUTHOR]

The energy of G is defined as the sum of absolute value of all eigenvalues of the adjacency matrix A(G). Let B²(n, a, b, p) be the set of all bicyclic graphs on n vertices with p pendent vertices and two cycles Ca and Cb which have unique common vertex u0, Bθ²(n, a, b, p) the graph class obtained by coinciding the common vertex u0 of Ca and Cb with the center of the star Sn-(a + b - 1)+1, and Bµ² (n, a, b, p) the set obtained by coinciding the common vertex u0 of Ca and Cb with the center of the star Sp and connecting a pendent path Pn - (a + b -1)-(p - 1) on point u0. In this paper, it is obtained that Bθ² (n, a, b, p) has the minimal energy in all graphs which have only pendent vertices except two cycles, and Bµ² (n, a, b, p) has the minimal energy in all graphs which have prescribed cycles' length and pendent vertices. [ABSTRACT FROM AUTHOR]