A general graph polynomial P(G, x) is introduced. It is proved that ddxP(G,x)= ∑v∈V(G) P(G−v,x). Special cases of this result are the previously reported first-derivative formulas for a number of graph polynomials: characteristic, matching, independence, clique polynomials, etc.
%0 Journal Article
%1 li95
%A Li, Xueliang
%A Gutman, Ivan
%D 1995
%J Discrete Applied Mathematics
%K algebraic.graph.theory characteristic derivative graph.theory matching polynomial sachs.theorem
%N 3
%P 293--297
%R 10.1016/0166-218X(95)00121-7
%T A Unified Approach to the First Derivatives of Graph Polynomials
%V 58
%X A general graph polynomial P(G, x) is introduced. It is proved that ddxP(G,x)= ∑v∈V(G) P(G−v,x). Special cases of this result are the previously reported first-derivative formulas for a number of graph polynomials: characteristic, matching, independence, clique polynomials, etc.
@article{li95,
abstract = {A general graph polynomial P(G, x) is introduced. It is proved that ddxP(G,x)= ∑v∈V(G) P(G−v,x). Special cases of this result are the previously reported first-derivative formulas for a number of graph polynomials: characteristic, matching, independence, clique polynomials, etc. },
added-at = {2015-05-12T13:14:34.000+0200},
author = {Li, Xueliang and Gutman, Ivan},
biburl = {https://www.bibsonomy.org/bibtex/212d995db3cdeb5edfdc7428ce700f7c2/ytyoun},
doi = {10.1016/0166-218X(95)00121-7},
interhash = {b4f66b30507e87ee9da46001e743f125},
intrahash = {12d995db3cdeb5edfdc7428ce700f7c2},
issn = {0166-218X},
journal = {Discrete Applied Mathematics },
keywords = {algebraic.graph.theory characteristic derivative graph.theory matching polynomial sachs.theorem},
number = 3,
pages = {293--297},
timestamp = {2016-12-03T05:31:42.000+0100},
title = {A Unified Approach to the First Derivatives of Graph Polynomials },
volume = 58,
year = 1995
}