The harmonic index H(G) , of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G. We present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in Caterpillars withf diameter 4.
Iranmanesh,M and Saheli,M . (2015). On the Harmonic Index and Harmonic Polynomial of Caterpillars with Diameter Four. Iranian Journal of Mathematical Chemistry, 6(1), 41-49. doi: 10.22052/ijmc.2015.9044
MLA
Iranmanesh,M , and Saheli,M . "On the Harmonic Index and Harmonic Polynomial of Caterpillars with Diameter Four", Iranian Journal of Mathematical Chemistry, 6, 1, 2015, 41-49. doi: 10.22052/ijmc.2015.9044
HARVARD
Iranmanesh M, Saheli M. (2015). 'On the Harmonic Index and Harmonic Polynomial of Caterpillars with Diameter Four', Iranian Journal of Mathematical Chemistry, 6(1), pp. 41-49. doi: 10.22052/ijmc.2015.9044
CHICAGO
M Iranmanesh and M Saheli, "On the Harmonic Index and Harmonic Polynomial of Caterpillars with Diameter Four," Iranian Journal of Mathematical Chemistry, 6 1 (2015): 41-49, doi: 10.22052/ijmc.2015.9044
VANCOUVER
Iranmanesh M, Saheli M. On the Harmonic Index and Harmonic Polynomial of Caterpillars with Diameter Four. Iranian J. Math. Chem.. 2015;6(1):41-49. doi: 10.22052/ijmc.2015.9044
