TY - JOUR

T1 - δ-Complement of a Graph

AU - Pai, Amrithalakshmi

AU - Rao, Harshitha A.

AU - D’Souza, Sabitha

AU - Bhat, Pradeep G.

AU - Upadhyay, Shankar

N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/4/1

Y1 - 2022/4/1

N2 - Let G(V,X) be a finite and simple graph of order n and size m. The complement of G, denoted by G¯¯¯, is the graph obtained by removing the lines of G and adding the lines that are not in G. A graph is self-complementary if and only if it is isomorphic to its complement. In this paper, we define δ-complement and δ′-complement of a graph as follows. For any two points u and v of G with degu=degv remove the lines between u and v in G and add the lines between u and v which are not in G. The graph thus obtained is called δ-complement of G. For any two points u and v of G with degu≠degv remove the lines between u and v in G and add the lines between u and v that are not in G. The graph thus obtained is called δ′-complement of G. The graph G is δ(δ′)-self-complementary if G≅Gδ(G≅Gδ′). The graph G is δ(δ′)-co-self-complementary if Gδ≅G¯¯¯(Gδ′≅G¯¯¯). This paper presents different properties of δ and δ′-complement of a given graph.

AB - Let G(V,X) be a finite and simple graph of order n and size m. The complement of G, denoted by G¯¯¯, is the graph obtained by removing the lines of G and adding the lines that are not in G. A graph is self-complementary if and only if it is isomorphic to its complement. In this paper, we define δ-complement and δ′-complement of a graph as follows. For any two points u and v of G with degu=degv remove the lines between u and v in G and add the lines between u and v which are not in G. The graph thus obtained is called δ-complement of G. For any two points u and v of G with degu≠degv remove the lines between u and v in G and add the lines between u and v that are not in G. The graph thus obtained is called δ′-complement of G. The graph G is δ(δ′)-self-complementary if G≅Gδ(G≅Gδ′). The graph G is δ(δ′)-co-self-complementary if Gδ≅G¯¯¯(Gδ′≅G¯¯¯). This paper presents different properties of δ and δ′-complement of a given graph.

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U2 - 10.3390/math10081203

DO - 10.3390/math10081203

M3 - Article

AN - SCOPUS:85130717952

SN - 2227-7390

VL - 10

JO - Mathematics

JF - Mathematics

IS - 8

M1 - 1203

ER -