TY - JOUR
T1 - Even harmonious labelings of disjoint graphs with a small component
AU - Gallian, Joseph A.
AU - Stewart, Danielle
N1 - Publisher Copyright:
© 2015 Kalasalingam University.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - A graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(. x). +. f(. y). (mod. q), the resulting edge labels are distinct. If G is a tree, exactly one label may be used on two vertices. Over the years, many variations of harmonious labelings have been introduced.We study a variant of harmonious labeling. A function f is said to be a properly even harmonious labeling of a graph G with q edges if f is an injection from the vertices of G to the integers from 0 to 2(q-1) and the induced function f * from the edges of G to 0, 2, . . ., 2(q-1) defined by f * (xy)=f(x)+f(y)(mod2q) is bijective. We investigate the existence of properly even harmonious labelings of families of disconnected graphs with one of C 3 , C 4 , K 4 or W 4 as a component.
AB - A graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(. x). +. f(. y). (mod. q), the resulting edge labels are distinct. If G is a tree, exactly one label may be used on two vertices. Over the years, many variations of harmonious labelings have been introduced.We study a variant of harmonious labeling. A function f is said to be a properly even harmonious labeling of a graph G with q edges if f is an injection from the vertices of G to the integers from 0 to 2(q-1) and the induced function f * from the edges of G to 0, 2, . . ., 2(q-1) defined by f * (xy)=f(x)+f(y)(mod2q) is bijective. We investigate the existence of properly even harmonious labelings of families of disconnected graphs with one of C 3 , C 4 , K 4 or W 4 as a component.
KW - Even harmonious labelings
KW - Graph labelings
KW - Harmonious labelings
KW - Properly even harmonious labelings
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U2 - 10.1016/j.akcej.2015.11.016
DO - 10.1016/j.akcej.2015.11.016
M3 - Article
AN - SCOPUS:84951815977
VL - 12
SP - 204
EP - 215
JO - AKCE International Journal of Graphs and Combinatorics
JF - AKCE International Journal of Graphs and Combinatorics
SN - 0972-8600
IS - 2-3
ER -