VB {(1,1,1,1),(1,1,1,0),(1,1,0,0),(1,0,0,0)}-Cordial Labeling of F-tree, Y-tree, key graph and spider graph

Ponraj, R; Jeya, R

doi:10.21608/ejmaa.2025.399090.1363

VB {(1,1,1,1),(1,1,1,0),(1,1,0,0),(1,0,0,0)}-Cordial Labeling of F-tree, Y-tree, key graph and spider graph

Document Type : Regular research papers

Authors

Sri Paramakalyani College

10.21608/ejmaa.2025.399090.1363

Abstract

Let G be a (p, q) graph. Let V be an inner product space with basis S. We
denote the inner product of the vectors x and y by < x, y >. Let ϕ : V (G) → S be a
function.For edge uv assign the label < ϕ(u), ϕ(v) >. Then ϕ is called a vector basis
S-cordial labeling of G (VB S-cordial labeling) if |ϕx − ϕy| ≤ 1 and |γi − γj | ≤ 1 where
ϕx denotes the number of vertices labeled with the vector x and γi denotes the number
of edges labeled with the scalar i. A graph which admits a vector basis S-cordial labeling
is called a vector basis S-cordial graph (VB S-cordial graph). We have studied in this paper VB S-Cordial labeling and we find the
existence of VB {(1,1,1,1),(1,1,1,0),(1,1,0,0),(1,0,0,0)}-cordial labeling of Y-tree, F-tree,
key graph, generalized key graph, spider graph, Hn and K1,m@2Pn.

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