| Two Factorization Theorems of Adjoint Polynomials of Graphs with Application |
| Received:December 04, 2000 |
| Key Words:
chromatic polynomial adjoint polynomial factorization chromatically equivalence chromatically uniqueness
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| Abstract: |
| Let G be a connected graph of order p and Pm be a path with m vertices. Let Skm+1G(i) denote the graph consisting of rG and the star Sk+1 by coinciding the ith vertex of everyone of rG with k-1 vertices of degree 1 of Sk+1; let Gi1S*(q,km) denote the graph obtained from a graph G of order 1 and Skm+1p(1) by coinciding the vertex vil of G with the vertex of degree k of Skm+1p(1). We give and prove that factorization theory of adjoint polynomials of graphs Skm+1G(i)∪(k-1)K1 and Gi1S*(q,km),and we obtain some structure characteristics of the chromatically equivalent graphs of their complements. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2003.02.030 |
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