on vertex balance index set of some graphs
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abstract
let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper we completely determine the vertex balance index set of kn, km,n, cn×p2 and complete binary tree.
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 39
issue 4 2013
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