textabstractCancer is the leading cause of death that touches us all, either directly or indirectly. It is estimated that the number of newly diagnosed cases in the Netherlands will increase to 123,000 by the year 2020. General Dutch statistics are similar to those in the UK, i.e. over the last ten years, the age-standardised incidence rate1 has stabilised at around 355 females and 415 males per 100,000. Figure 1 shows the cancer incidence per gender. In the UK, the rise in lifetime risk of cancer is more than one in three and depends on many factors, including age, lifestyle and genetic makeup.
In this paper we define cycle-star graphCSk;n k to be a graph onn vertices consisting of the cycle of lengthk andn k leafs appended to the same vertex of the cycle. Also, we define cycle-path graphCPk;n k to be a graph onn vertices consisting of the cycle of lengthk and of path on n k vertices whose one end is linked to a vertex on a cycle. We establish that cycle- star graphCS3;n 3 is the only maximal graph with respect to additively weighted Harary index among all unicyclic graphs on n vertices, while cycle-path graph CP3;n 3 is the only minimal unicyclic graph (here n must be at least 5): The values of additively weighted Harary index for extremal unicyclic graphs are established, so these values are the upper and the lower bound for the value of additively weighted Harary index on the class of unicyclic graphs onn vertices. 2010 Mathematics Subject Classification: 05C35
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