Quotient cordial labeling of some star related graphs (Q2831557)

In this paper, the authors discuss a new type of labeling of graphs called quotient cordial labeling and investigate some star-related graphs. In the introductory part, the authors give preliminary results which are required to prove the main theorems. After introducing the new concept ``quotient cordial'' of graph labeling in their previous work, the authors successfully examine the behaviour of certain classes of graphs, like subdivided stars \(S(K_{1,n})\), subdivided bistars \(S(B_{n,n})\), \(K_{1,n} \cup S(K_{1,n})\), \(S(K_{1,n}) \cup B_{n,n}\), \(Spl(K_{1,n}) \cup K_{1,n}\), \(K_{1,n} \cup B_{n,n}\), \(S(K_{1,n}) \cup S(K_{1,n})\), \(Spl(K_{1,n}) \cup S(K_{1,n})\), \(Spl(K_{1,n}) \cup B_{n,n}\) and some star-related graphs, in this present paper.NEWLINENEWLINENEWLINENoteworthy aspects: The topic is presented systematically and in an orderly way. The use of table is praiseworthy as they summarize a lot of aspects in the proof. The detailed reference given is appreciated. On the whole the paper appears to be creative and innovative piece of work. NEWLINENEWLINENEWLINE Some suggestions: Certain characteristics of carelessness are found in editing the paper; placing the serial numbers of the theorem, commas, fullstops etc. After 2.5, serial numbers are missing; so Theorem 2.14 should be labeled as 2.6 (Theorem 2.14\(\longrightarrow\)2.6) and so on. Page 314: Theorem 2.1 -- line 2 : \(v \longrightarrow v_{i}\). Page 314: Theorem 2.2 -- line 2 : \(V(S(K_{1,n})) \longrightarrow V(S(B_{n,n}))\). Page 316: Theorem 2.5 -- line 3 : \(2n+2 \longrightarrow 2n+3\). Page 317: Theorem 2.15 \(\longrightarrow\) Theorem 2.7 : line 2: \(u_{i}x \longrightarrow ux\). Page 318: Theorem 2.16 \(\longrightarrow\) Theorem 2.8 : line 1, line 4: \(K_{1,m} \longrightarrow K_{1,n}\). Page 320: Theorem 2.19 \(\longrightarrow\) Theorem 2.11 : line 4: \(K_{1,m} \longrightarrow K_{1,n}\). Page 321: Theorem 2.21 \(\longrightarrow\) Theorem 2.13 : line 2: remove `\(\cup S(K_{1,n})\)'. Some more figures would have been welcome for a better presentation of the paper.