%0 Journal Article %1 Gutman %A Gutman, Ivan %A Li, Xueliang %A Zhang, Heping %D 1993 %I University of Belgrade, Serbia %J Publikacije Elektrotehničkog fakulteta. Serija Matematika %K bipartite characteristic derivative graph.theory matching polynomial sachs.theorem %N 4 %P 97--102 %R 10.2307/43666364 %T On a Formula Involving the First Derivative of the Characteristic Polynomial of a Graph %U http://www.jstor.org/stable/43666364 %X Let G be a graph on n vertices and ɸ(G, λ) its characteristic polynomial. Let $łeft( G,x,y \right) = y^n/2łeft( G,xy^ - 1/2 \right)$. A problem was recently posed (Discrete Math.88 (1991) 105-106) to find an expression for ϑɸ(G, x, y)/ϑy when G is a bipartite graph. We obtain such an expression and show that it holds for both bipartite and non-bipartite graphs.

@article{Gutman, abstract = {Let G be a graph on n vertices and ɸ(G, λ) its characteristic polynomial. Let $\phi \left( {G,x,y} \right) = {y^{n/2}}\phi \left( {G,x{y^{ - 1/2}}} \right)$. A problem was recently posed (Discrete Math.88 (1991) 105-106) to find an expression for ϑɸ(G, x, y)/ϑy when G is a bipartite graph. We obtain such an expression and show that it holds for both bipartite and non-bipartite graphs.}, added-at = {2017-01-02T11:07:15.000+0100}, author = {Gutman, Ivan and Li, Xueliang and Zhang, Heping}, biburl = {https://www.bibsonomy.org/bibtex/28424e9ae8ef3a8d895b9112693397197/ytyoun}, doi = {10.2307/43666364}, interhash = {f8aad6650f2131c8c67186f244d4a154}, intrahash = {8424e9ae8ef3a8d895b9112693397197}, issn = {03538893, 24060852}, journal = {Publikacije Elektrotehničkog fakulteta. Serija Matematika}, keywords = {bipartite characteristic derivative graph.theory matching polynomial sachs.theorem}, number = 4, pages = {97--102}, publisher = {University of Belgrade, Serbia}, timestamp = {2017-08-11T10:24:47.000+0200}, title = {On a Formula Involving the First Derivative of the Characteristic Polynomial of a Graph}, url = {http://www.jstor.org/stable/43666364}, year = 1993 }