On the Differential Polynomial of a Graph

  • Ludwin A. Basilio-HernándezEmail author
  • Walter Carballosa
  • Jesús Leaños
  • José M. Sigarreta


We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial \(B(G;x):={\sum}_{k=-n}^{\partial(G)}B_k(G)x^{n+k}\), where Bk(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G; x) and its coefficients. In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G.


Graph polynomial differential of a graph 

MR(2010) Subject Classification

05C31 05C69 


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We would like to thank the referees for a careful reading of the manuscript and for some helpful suggestions.


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ludwin A. Basilio-Hernández
    • 1
    Email author
  • Walter Carballosa
    • 2
    • 3
  • Jesús Leaños
    • 1
  • José M. Sigarreta
    • 4
  1. 1.Unidad Académica de MatemáticasUniversidad Autónoma de ZacatecasZacatecasMéxico
  2. 2.Department of Mathematics and StatisticsFlorida International UniversityMiamiUSA
  3. 3.Department of MathematicsMiami Dade CollegeMiamiUSA
  4. 4.Facultad de MatemáticasUniversidad Autónoma de GuerreroAcalpulco Gro.México

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