3-vertex full balance index set of graphs

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Let G be a graph with vertex set V (G) and edge set X(G). Consider the set A = {0, 1, 2}. A labeling f: V (G) → A induces a partial edge labeling f: X(G) → A defined by f(xy) = f(x), if and only if f(x) = f(y), for each edge xy ∈ X(G). For i ∈ A, let vf (i) = |{v ∈ V (G): f(v) = i}| and ef (i) = |{e ∈ X(G): f (e) = i}|. A labeling f of a graph G is said to be 3-vertex friendly if |vf (i) − vf (j)| ≤ 1, for all i ∈ {0, 1, 2}. The 3-vertex full balance index set of a graph G is denoted by F BI3v (G) and is defined as {ef(i) − ef(j), for i, j = 0, 1, 2: fruns over all 3-vertex friendly labeling f of G}. In paper, we study 3-vertex full balance index set and 3-vertex balance index set of some families of graph.

Original languageEnglish
Pages (from-to)3247-3264
Number of pages18
JournalAdvances in Mathematics: Scientific Journal
Issue number6
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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