Nehru E- Journal A Journal of Nehru Arts and Science College (Autonomous) Journal Home Page: http://nehrucolleges.net/jo.html ISSN: 2349-952 Research Article ol 5 issue (27) (Jan - July 27) CORDIAL LABELING OF RELATED GRAPHS P.Premkumar and S.Mohammed Shanawaz 2,, Asst. Prof., Dept. Of Maths, Nehru Arts and Science College, Coimbatore 64 5, India Keywords: Cloud storage, Auditing, Data integrity, third party auditor Abstract In this article we prove that the star of is cordial for all Introduction: For the basic definitions we follow J.A.Bondy and U.S.R.Murty and Frank Harary[4]. The main definitions are followed by G..Ghodasara et al. [7]. Key words: Bipartite graph, Star graph, Star of a graph, Cordial labeling. Theorem 3.: Star of complete bipartite graph is cordial. Proof: Let be the star of complete bipartite graph. Let and be the partitions of the vertex set of the central copy of complete bipartite graph in G. Let be successive vertices of the set and be successive vertices of the set (in counter clockwise direction). Let and be the partitions of the vertex set of i th copy of complete bipartite graph in G (except central one). Let be successive vertices of the set and let be successive vertices of the set. Let be the edge joining central copy and i th copy of. Moreover let denote the vertices of the copy of which is joined to vertex with label of the central copy of by an edge and let denote the vertices of the copy of which is joined to vertex with label of the central copy of, where. To define required labeling we consider the following cases: Case : For, Case 2: For, 22
The graph G under consideration satisfies the condition and in each case which is shown in Table I. Hence the graph G is cordial graph. Let where TABLE: I... b..2. ertex conditions..3. Edge conditions..4.,3..5...6...7.,2..8...9. Illustration 3.: The cordial labeling of star to complete bipartite graph of Theorem 3.. It is the case related to. is shown in figure 3.(b) as an illustration for the proof u 4 u 3 u 65 u 64 u 5 u 2 u 66 u 63 u 6 u u 6 u62 u 23 u 22 u 56 u 55 u 24 u 2 u 5 u 54 u 25 u 26 u 52 u 53 u 32 u 3 u 4 u 46 u 33 u 36 u 42 u 45 u 34 u 35 u 43 u 44 Figure 3.(a)
Figure 3.(b) : Cordial labeling of star of complete bipartite graph Thus and. Hence the above graph is cordial. Illustration 3.2: The cordial labeling of star to complete bipartite graph is shown in figure 3.2 as an illustration for the proof of Theorem. It is the case related to.
Figure 3.2 : Cordial labeling of star of complete bipartite graph Thus and. Hence the above graph is cordial. Illustration 3.3: The cordial labeling of star to complete bipartite graph is shown in figure 3.3 as an illustration for the proof of Theorem. It is the case related to
Figure 3.3 : Cordial labeling of star of complete bipartite graph Thus and. Hence the above graph is cordial..illustration 3.4: The cordial labeling of star of complete bipartite graph illustration for the proof of Theorem. It is the case related to is shown in figure 3.4 as an
Figure 3.4 : Cordial labeling of star of complete bipartite graph Thus and. Hence the above graph is cordial.
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