Hosoya Polynomial of the q-vertex Join

Eunice Gogo Mphako-Banda, Thokozani Ncambalala


The Hosoya polynomials of diameter 1 and diameter 2 graphs are known. We extend the concept of  a vertex join of a graph to q-vertex join. Then we give the formula of the Hosoya polynomial of a $q$-vertex join of a complete graph and the formula of the Hosoya polynomial of a q-vertex join of a diameter 2 graph.


Diameter; distance; Hosoya polynomial; $q$-vertex join; Wiener index

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