@article{MAKHILLIJSC201611621374,
    title = {L(0,1) and L(1,1) Labeling Problems on Circular-Arc Graphs},
    journal = {International Journal of Soft Computing},
    volume = {11},
    number = {6},
    pages = {343-350},
    year = {2016},
    issn = {1816-9503},
    doi = {ijscomp.2016.343.350},
    url = {https://makhillpublications.co/view-article.php?issn=1816-9503&doi=ijscomp.2016.343.350},
    author = {Madhumangal and},
    keywords = {Frequency assignment,L(0, 1)-labeling,L(1, 1)-labeling,circular-arc,graph,span},
    abstract = {An L(0, 1)-labeling of a graph G = (V, E) is a function f from the vertex set V(G) to the set of non-negative integers such that /f(x)-f(y)/&#8805;0 if d(x, y) = 1 and /f(x)-f(y)/&#8805;1 if d(x, y) = 2. The L(0, 1)-labeling number of a graph G, denoted by &#955;<SUB>0, 1</SUB> (G) is the difference between highest and lowest labels used. Similarly, L(1, 1)-labeling of a graph G = (V, E) is a function f from its vertex set V to the set of non-negative integers such that /f(x)-f(y)/&#8805;1 if d(x, y) = 1 or 2. The span of an L(1, 1)-labeling f of G is max{f(v): v&#8712;V}. The L(1, 1)-labeling number &#955;<SUB>1, 1</SUB> (G) of G is the smallest non-negative integer k such that G has a L(1, 1)-labeling of span k. In this study, for any circular-arc graph G, we have shown that &#955;<SUB>0, 1</SUB>(G)&#8804;&#916; and &#955;<SUB>1, 1</SUB>(G)&#8804;2 where &#916; represents the degree of the graph G. Also two algorithms are designed to label a circular-arc graph by maintaining L(0, 1)-and L(1, 1)-labeling conditions. The running time of these algorithms are O(n&#916;<SUP>2</SUP>) and O(n&#916;), respectively where n represent the number of vertices of G.}
    }