SIGNED SUM CORDIAL LABELING OF GRAPHS

Year 2025, Volume: 15 Issue: 10, 2556 - 2566, 01.10.2025

K. Jeya Daisy , P. Princy Paulson P. Jeyanthi

Abstract

The notion of signed product cordial labeling was introduced in 2011 and further studied by several researchers. Inspired by this notion, we define a new concept namely signed sum cordial labeling as follows: A vertex labeling of a graph $G$, $f: V(G) \rightarrow \left\lbrace -1,+1 \right\rbrace $ with induced edge labeling $f^\ast : E(G) \rightarrow \left\lbrace -2,0,+2 \right\rbrace $ defined by $f^\ast (uv) = f(u) + f(v) $ is signed sum cordial labeling if $ | v_f (-1) - v_f (+1)| \leq 1 $ and $| e_{f^\ast} (i)- e_{f^\ast} (j)| \leq 1 $ for $i,j \in \left\lbrace -2,0,+2 \right\rbrace $, where $v_f(-1)$ is the number of vertices labeled with -1, $v_f(+1)$ is the number of vertices labeled with +1, $e_{f^\ast}(-2)$ is the number of edges labeled with -2, $e_{f^\ast}(0)$ is the number of edges labeled with 0 and $ e_{f^\ast}(+2)$ is the number of edges labeled with +2. A graph G is signed sum cordial if it admits signed sum cordial labeling. In this paper, we investigate the signed sum cordial behaviour of some standard graphs.

Keywords

cordial labeling , signed cordial labeling , signed product cordial labeling , signed sum cordial labeling

References

• Reference 1 Atef Abd El-hay and Aya Rabie, (2022), Signed product cordial labeling of corona product between paths and second power of fan graphs, Italian Journal of Pure and Applied Mathematics, 48, pp. 287-294.
• Reference 2 Cahit, I., (1987), cordial graphs: A weaker version of graceful and harmonious graphs, Ars Combinatoria, 23(3), pp.201-207.
• Reference3 Devaraj, J. and Prem Delphy, P., (2011), On signed cordial graph, International Journal of Mathematical Sciences and Application, 1(3), pp. 1159-1167.
• Reference4 Elrokh, A. and Rabie, A., (2020), The signed product cordial of the sum and union of the fourth power of paths with cycles, South Asian Research Journal of Engineering and Technology, 2(2), pp. 10-16.
• Reference5 Gallian, J. A., (2023), A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, # DS6.
• Reference6 Harary, F., (1972), Graph theory, Addison-Wesley, Reading, Massachusetts.
• Reference7 Harary, F., (1960), On the consistency of certain graph- theoretic axioms, Journal of Mathematical Psychology, 3(2), pp. 151-155.
• Reference8 Jayapal Baskar Babujee and Shobana Loganathan, (2011), On signed product cordial labeling, Scientific Research Journal on Applied Mathematics, 2, pp. 1525-1530.
• Reference9 Jude Annie Cynthia, V. and Padmavathy, E., (2018), Signed product cordial labeling of comb related architectures, International Journal of Pure and Applied Mathematics, 120(7), pp. 235-243.
• Reference10 Karishma Raval, K. and Udayan Prjapati, M., (2023), Signed product cordial labeling of some fractal graphs, Gradiva Review Journal, 8(11), pp. 537-546.
• Reference11 Lawrence Rozario Raj, P. and Lawrence Joseph Manoharan, R., (2012), Signed product cordial graphs in the context of arbitrary supersubdivision, Scientia Magna, 8(4), pp. 77-87.
• Reference12 Rosa, A., (1966), On certain valuations of the vertices of a graph, Theory of graphs, International Symposium, Rome, pp. 349-355.
• Reference13 Shobana, L. and Vasuki, B., (2017), Signed product cordial labeling on some connected graphs, International Journal of Pure and Applied Mathematics, 113(13), pp. 198-207.
• Reference14 Soundar Rajan, S. and Baskar Babujee, J., (2023), Further results on signed product cordial labeling, Revista Argentina de Clinica Psicologica, XXXII(1), pp. 1-4.
• Reference15 Ulaganathan, P. P., Selvam, B., Vijaya Kumar, P., (2016), Signed product cordial labeling in duplicate graphs of bistar, double Star and triangular Ladder Graph, International Journal of Mathematics Trends and Technology, 33(1), pp. 19-24.
• Reference16 Talal Ali Al-Hawary, Sumaya H. Al-Shalalden and Muhammad Akram, (2023), Certain Matrices and Energies of Fuzzy Graphs. TWMS JPAM V.14, N.1, pp.50-68.