| Abstrak/Abstract |
Given a graph B = (V (B), E(B)) with the vertex
set V (B) and the edge set E(B). A vertex labelling of a
simple, connected, and undirected B, g : V (B) → {1, 2, . . . , q}
is called an edge irregular q-labelling on B if two arbitrary
edges uv, u′
v
′
in B have different weights, where the weight
of edge uv is defined as ωg(uv) = g(u) + g(v). Then the
edge irregularity strength of B, denoted by es(B) is defined
as the smallest integer q such that B can be labelled by an
edge irregular q-labelling. Furthermore, the edge irregularity
strength in the graph B with maximum degree ∆(B) satisfies
es(B) ≥ max
⌈
|E(B)|+1
2
⌉, ∆(B)
. In this study, we develop
an edge irregular q-labelling and determine the exact value
of the edge irregularity strength of triangular book graph
Bp(C3), rectangular book graph Bp(C4), pentagonal book
graph Bp(C5). We show that the exact value of the es(B)
of Bp(C3), Bp(C4), Bp(C5) is equal to p + 2, ⌈
3p+2
2
⌉, ⌈
4p+2
2
⌉,
respectively. We also investigate an edge irregular q-labelling
and determine the exact value of the edge irregularity strength
of book graph Bp(Cm) with additional (m − 2)p pendant
edges and with additional p pendant edges for m ≥ 6.
For any book graph Bp(Cm) for m ≥ 6, we obtain that
⌈
(m−1)p+2
2
⌉ ≤ es(Bp(Cm)) ≤ ⌈ mp+2
2
⌉.
|
