Further results on mean cordial labeling for three star graph
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A vertex labeling h : V (G)→{0, 1, 2} is said to be a mean cordial labeling of G if it induces an edge labeling h* given by such that | vh(b)-vh(p)| ≤ 1 and | eh(b)-eh(p)|≤1, b, p∈{0, 1, 2}, where vh(r) and eh(r) denote the number of vertices and edges respectively labeled with r (r = 0, 1, 2). A graph G is said to be a mean cordial graph if it admits a mean cordial labeling. In this paper we proved that three star graph is a mean cordial labeling. If r = s < t, the three star graph K1,r ∧K1;s ∧K1;t is a mean cordial graph if and only if |s-t|≤3r+6 for 3r+s-7≤t≤3r+s+6; r = 1, 2, 3, …. and s = 1, 2, 3,….
Abstract
A vertex labeling h : V (G)→{0, 1, 2} is said to be a mean cordial labeling of G if it induces an edge labeling h* given by such that | vh(b)-vh(p)| ≤ 1 and | eh(b)-eh(p)|≤1, b, p∈{0, 1, 2}, where vh(r) and eh(r) denote the number of vertices and edges respectively labeled with r (r = 0, 1, 2). A graph G is said to be a mean cordial graph if it admits a mean cordial labeling. In this paper we proved that three star graph is a mean cordial labeling. If r = s < t, the three star graph K1,r ∧K1;s ∧K1;t is a mean cordial graph if and only if |s-t|≤3r+6 for 3r+s-7≤t≤3r+s+6; r = 1, 2, 3, …. and s = 1, 2, 3,….
참고문헌 (7)
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