On product-cordial index sets and friendly index sets of 2-regular graphs and generalized wheels |
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| Authors: | Harris Kwong Sin Min Lee Ho Kuen Ng |
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| Institution: | (1) Department of Mathematical Science, SUNY Fredonia, Fredonia, NY 14063, USA;(2) Department of Computer Science, San Jose State University, San Jose, CA 95192, USA;(3) Department of Mathematics, San Jose State University, San Jose, CA 95192, USA |
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| Abstract: | A vertex labeling f: V → ℤ2 of a simple graph G = (V, E) induces two edge labelings f
+, f*: E → ℤ2 defined by f
+(uυ) = f(u) + f(υ) and f*(uυ) = f(u)f(υ). For each i ∈ ℤ2, let υ
f
(i) = |{υ ∈ V: f(υ) = i}|, e
f
+(i) = |{e ∈ E: f
+(e) = i}| and e*
f
(i) = |{e ∈ E: f*(e) = i}|. We call f friendly if |υ
f
(0) − υ
f
(1)| ≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets {|e
f
+
f(0) − e
f
+(1)|: f is friendly} and {|e*
f
(0) − e*
f
(1)|: f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index
sets of 2-regular graphs and generalized wheel graphs. |
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| Keywords: | Friendly index set product cordial index set 2-regular graphs generalized wheels |
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