Formulas for the characteristic polynomial coefficients of the pendant graphs of linear chains,cycles and stars |
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Authors: | Piyali Ghosh |
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Institution: | Department of Chemistry, The University of Burdwan, Burdwan - 713104, India |
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Abstract: | Formulas for the characteristic polynomial (CP) coefficients of three classes of (n + p)-vertex graphs, i.e. linear chains, cycles and stars where p pendant vertices are attached to n base vertices in one-to-one correspondence (p = 0, 1, 2, …, n), have been developed. Such pendant graphs become reciprocal graphs for linear chains and cycles if p = n. The n-vertex star graphs follow the same rule as paths and cycles, they become reciprocal on adding a pendant vertex to each of n vertices. The formulas so developed have been expressed in matrix product and in analytical forms for the three classes of graphs that require only the values of n and p for calculation of the respective CP coefficients. Such formulas have the general applicability for a large variety of molecular graphs with varying n and p and have been shown to be reduced to the corresponding formulas for reciprocal graphs that are the special cases of the graphs discussed here. |
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Keywords: | characteristic polynomial pendant graphs reciprocal graphs |
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