TY - JOUR

T1 - Some results on generalized self-complementary graphs

AU - Gowtham, H. J.

AU - Upadhyay, Shankar N.

AU - D'Souza, Sabitha

AU - Bhat, Pradeep G.

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - Let P = {V1,V2,...,Vk} be a partition of vertex set V of order k ≥ 2 of a graph G(V,E). The k-complement of G denoted by GkP is defined as for all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj in G and add the edges between Vi and Vj which are not in G. The graph G is called k-self-complementary if G≅GkP. For a graph G, k(i)-complement of G denoted by Gk(i)P is defined as for each Vr remove the edges of G inside Vr and add the edges of G¯ by joining the vertices of Vr. The graph G is called k(i)-self-complementary if G≅Gk(i)P for some partition P of order k. In this paper, we determine generalized self-complementary graphs of forest, double star and unicyclic graphs.

AB - Let P = {V1,V2,...,Vk} be a partition of vertex set V of order k ≥ 2 of a graph G(V,E). The k-complement of G denoted by GkP is defined as for all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj in G and add the edges between Vi and Vj which are not in G. The graph G is called k-self-complementary if G≅GkP. For a graph G, k(i)-complement of G denoted by Gk(i)P is defined as for each Vr remove the edges of G inside Vr and add the edges of G¯ by joining the vertices of Vr. The graph G is called k(i)-self-complementary if G≅Gk(i)P for some partition P of order k. In this paper, we determine generalized self-complementary graphs of forest, double star and unicyclic graphs.

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U2 - 10.1142/S1793830922500653

DO - 10.1142/S1793830922500653

M3 - Article

AN - SCOPUS:85147830146

SN - 1793-8309

VL - 15

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

IS - 1

M1 - 2250065

ER -