Journal Name:
- European Journal of Pure and Applied Mathematics
Key Words:
| Author Name | University of Author |
|---|---|
Abstract (2. Language):
Let G = (V, E) be a given connected simple (p, q)-graph, and an arbitrary nonempty subset
M ⊆ V(G) of G and for each v ∈ V(G), define NM
j [u] = {v ∈ M : d(u, v) = j}. Clearly, then Nj[u] =
NV(G)
j [u]. B.D. Acharya [2] defined the M-eccentricity of u as the largest integer for which NM
j [u] 6= ;
and the p ×(dG +1) nonnegative integer matrix DM
G = (|NM
j [vi]|), called the M-distance neighborhood
pattern (or, M-dnp) matrix of G. The matrix D∗M
G is obtained from DM
G by replacing each nonzero
entry by 1. Clearly, fM(u) = { j : NM
j [u] 6= ;}. Hence, in particular, if fM : u 7→ fM(u) is an injective
function, then the set M is a distance-pattern distinguishing set (or, a ‘DPD-set’ in short) of G and G is
a dpd-graph. If fM(u) − {0} is independent of the choice of u in G then M is an open distance-pattern
uniform (or, ODPU) set of G. A study of these sets is expected to be useful in a number of areas
of practical importance such as facility location [5] and design of indices of “quantitative structureactivity
relationships” (QSAR) in chemistry [3, 10]. This paper is a study of M-dnp matrices of a
dpd-graph.
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FULL TEXT (PDF):
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748-764