کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8902947 | 1632396 | 2018 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Unimodality of independence polynomials of the incidence product of graphs
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Given two graphs G and H, assume that V(G)={v1,v2,â¦,vn} and U is a subset of V(H). We introduce a new graph operation called the incidence product, denoted by GâHU, as follows: insert a new vertex into each edge of G, then join with edges those pairs of new vertices on adjacent edges of G. Finally, for every vertex viâV(G), replace it by a copy of the graph H
and join every new vertex being adjacent to vi to every vertex of U. It generalizes the line graph operation. We prove that the independence polynomial IGâHU;x=In(H;x)MG;xI2(HâU;x)I2(H;x),where M(G;x) is its matching polynomial. Based on this formula, we show that the incidence product of some graphs preserves symmetry, unimodality, reality of zeros of independence polynomials. As applications, we obtain some graphs so-formed having symmetric and unimodal independence polynomials. In particular, the graph Q(G) introduced by CvetkoviÄ, Doob and Sachs has a symmetric and unimodal independence polynomial.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 341, Issue 8, August 2018, Pages 2359-2365
Journal: Discrete Mathematics - Volume 341, Issue 8, August 2018, Pages 2359-2365
نویسندگان
Bao-Xuan Zhu,