A topological index is a number that connected to chemical composition in order correlate substance’s makeup with different physical characteristics, reactivity, or biological activity. It common model drugs and other substances as forms, trees, graphs. Certain physico-chemical features of better degree-based invariants. Predictions concerning the dynamics continuing pandemic may be made use gr...

The matching energy of a graph was introduced by Gutman and Wagner in 2012 and defined as the sum of the absolute values of zeros of its matching polynomial. Let θ(r, s, t) be the graph obtained by fusing two triples of pendant vertices of three paths Pr+2, Ps+2 and Pt+2 to two vertices. The graph obtained by identifying the center of the star Sn−g with the degree 3 vertex u of θ(1, g−3, 1) is ...

We show that for the edge ideals of the graphs consisting of one cycle or two cycles of any length connected through a vertex or a path, the arithmetical rank equals the projective dimension.

Article history: Received 7 February 2013 Accepted 15 October 2013 Available online 4 November 2013 Submitted by S. Kirkland

Du, Zhou and Trinajstić [J. Math. Chem., 48, pp. 697–703, 2010] proved that in the set of n-vertex connected unicyclic graphs G with n ≥ 3, for –1 ≤ α < 0, the graph consisting of a triangle and n – 3 pendant vertices adjacent to the same vertex of this triangle is the unique graph with the minimum general sum-connectivity index. In this paper, using a graph transformation and several inequalit...