TY - JOUR
T1 - Some results on super edge-magic deficiency of graphs
AU - Imran, M.
AU - Baig, A. Q.
AU - Fenovcíková, A. S.
N1 - Publisher Copyright:
© 2020 University of Kragujevac, Faculty of Science.
PY - 2020
Y1 - 2020
N2 - An edge-magic total labeling of a graph G is a bijection f: V (G) ∪ E(G) → [1, 2,..., V (G) + E(G)], where there exists a constant k such that f(u) + f(uv) + f(v) = k, for every edge uv ∈ E(G). Moreover, if the vertices are labeled with the numbers 1, 2,..., V (G) such a labeling is called a super edge-magic total labeling. The super edge-magic deficiency of a graph G, denoted by μs(G), is the minimum nonnegative integer n such that G ∪ nK1 has a super edge-magic total labeling or is defined to be ∞ if there exists no such n. In this paper we study the super edge-magic deficiencies of two types of snake graph and a prism graph Dn for n ≡ 0 (mod 4). We also give an exact value of super edge-magic deficiency for a ladder Pn x K2 with 1 pendant edge attached at each vertex of the ladder, for n odd, and an exact value of super edge-magic deficiency for a square of a path Pn for n ≥ 3.
AB - An edge-magic total labeling of a graph G is a bijection f: V (G) ∪ E(G) → [1, 2,..., V (G) + E(G)], where there exists a constant k such that f(u) + f(uv) + f(v) = k, for every edge uv ∈ E(G). Moreover, if the vertices are labeled with the numbers 1, 2,..., V (G) such a labeling is called a super edge-magic total labeling. The super edge-magic deficiency of a graph G, denoted by μs(G), is the minimum nonnegative integer n such that G ∪ nK1 has a super edge-magic total labeling or is defined to be ∞ if there exists no such n. In this paper we study the super edge-magic deficiencies of two types of snake graph and a prism graph Dn for n ≡ 0 (mod 4). We also give an exact value of super edge-magic deficiency for a ladder Pn x K2 with 1 pendant edge attached at each vertex of the ladder, for n odd, and an exact value of super edge-magic deficiency for a square of a path Pn for n ≥ 3.
KW - Block graph
KW - Corona of graphs
KW - Prism
KW - Snake graph
KW - Square of graph
KW - Super edge-magic deficiency
KW - Super edge-magic total labeling
UR - http://www.scopus.com/inward/record.url?scp=85087675255&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85087675255&partnerID=8YFLogxK
U2 - 10.46793/kgjmat2002.237i
DO - 10.46793/kgjmat2002.237i
M3 - Article
AN - SCOPUS:85087675255
SN - 1450-9628
VL - 44
SP - 237
EP - 249
JO - Kragujevac Journal of Mathematics
JF - Kragujevac Journal of Mathematics
IS - 2
ER -