Applied Mathematics & Information Sciences

Author Country (or Countries)

Saudi Arabia


The symmetric division deg (SDD) index of a graph G is the addition of the numbers (dvdu)−1[(dv)2 +(du)2] over all the edges uv of G, where dv and du represent degrees of the vertices v and u, respectively. A connected graph in which every edge lies on at most one cycle is usually referred to as a cactus graph. (Every tree as well as every unicyclic graph is a cactus graph; the converse is not generally true.) The primary goal of the present paper is to characterize the unique graph possessing the maximum value of the SDD index over the class of all cactus graphs with a fixed order and number of cycles.

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