TY - JOUR

T1 - Some results on super edge-magic deficiency of graphs

AU - Imran, M.

AU - Baig, A. Q.

AU - Fenovcíková, A. S.

N1 - Funding Information:
Also this research is supported by Slovak Science and Technology Assistance Agency under the contract No. APVV-15-0116 and by VEGA 1/0233/18.
Funding Information:
This research is supported by the Start-up Research Grant 2016 of United Arab Emirates University (UAEU), Al Ain, United Arab Emirates via Grant No. G00002233 and UPAR Grant of UAEU via Grant No. G00002590. Also this research is supported by Slovak Science and Technology Assistance Agency under the contract No. APVV-15-0116 and by VEGA 1/0233/18.
Funding Information:
Acknowledgements. This research is supported by the Start-up Research Grant 2016 of United Arab Emirates University (UAEU), Al Ain, United Arab Emirates via Grant No. G00002233 and UPAR Grant of UAEU via Grant No. G00002590.
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

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M3 - Article

AN - SCOPUS:85087675255

VL - 44

SP - 237

EP - 249

JO - Kragujevac Journal of Mathematics

JF - Kragujevac Journal of Mathematics

SN - 1450-9628

IS - 2

ER -