Bibliographic Details
| Title: |
ON THE TOTAL CHROMATIC NUMBER OF ODD LINE GRAPHS OF ODD COMPLETE GRAPHS. |
| Authors: |
Thatchayani, S.1 thatchu170@gmail.com, Geethalakshmi, S.1 geetha2611@gmail.com, Somasundaram, K.2 s_sundaram@cb.amrita.edu |
| Source: |
Advances & Applications in Discrete Mathematics. Apr2026, Vol. 43 Issue 3, p337-352. 16p. |
| Subjects: |
Complete graphs, Graph coloring |
| Abstract: |
≥a total coloring of a graphg = (ν,ε) entails the meticulous assignment of colors to both vertices and edges, ensuring that neither two adjacent vertices nor two adjacent edges receive the same color. furthermore, it requires that for each edge, the colors of its end-points and the edge itself must differ. the total chromatic number of a graph g, indicated as χ"(g) signifies the minimum number of colors required for such a total coloring. the renowned conjecture by behzad and vizing asserts that for any graph g, the inequality Δ (g) + 1 ≤ χ"(g) ≤ Δ(g) + 2 holds, where Δ(g) signifies the graph's maximum degree. in this paper, we obtain that odd line graphs of odd complete graphs L (Kn), where n = 2℘ + 1 and ℘ 3 (with ℘ being odd), can be adorned with a total coloring with Δ(L(Kn)) + 1 colors. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
