Journal of the Indonesian Mathematical Society has been acreditated by the General Directorate of Higher Education (DIKTI)

SK NO.:58/DIKTI/Kep/2013

### A FEW MORE PROPERTIES OF SUM AND INTEGRAL SUM GRAPHS

#### Abstract

The concepts of sum graph and integral sum graph were introduced by Harary [7], [8]. A sum graph is a graph whose vertices can be labeled with distinct positive integers so that the sum of the labels on each pair of adjacent vertices is the label of some other vertex. Integral sum graphs have the same definition except that the labels may be any integers. Harary [7], [8], gave examples of all orders of sum graphs and integral sum graphs , *n*Î*N*. The family of integral sum graph was extended by Vilfred (see [14]), and in this paper, we obtain a few properties of sum and integral sum graphs and two new families of integral sum graphs.

#### Keywords

#### Full Text:

PDF#### References

Amird Aczel, Fermat’s last theorem, Dell Publishing, NY, 1997, pp. 20.

Z. Chen, Harary’s conjecture on integral sum graphs, Discrete Math., 160 (1990), pp. 241-244.

Douglas B. West, Introduction to graph theory, Pearson Education, 2005.

M. N. Ellingham, Sum Graphs from trees, Ars Comb., 35 (1993), pp. 335-349.

J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Comb., 19 (2013), #DS6.

F. Harary, Graph Theory, Addison Wesley, Reading Mass., 1969.

F. Harary, Sum graphs and difference graphs, Cong. Num., 72 (1990), pp.101-108.

F. Harary, Sum graphs over all integers, Discrete Math., 124 (1994), pp. 99-105.

T. Nicholas, S. Somasundaram and V. Vilfred, Some results on sum graphs, J. Comb. Inf. & System Sci., 26 (2001), pp. 135–142.

V. Vilfred, L.W. Beineke and A. Suryakala, More properties of sum graphs, Graph Theory Notes of New York, MAA, 66 (2014), pp. 10-15.

V. Vilfred, R. Kala and A. Suryakala, (a,d)-Ascending subgraph decomposition of graphs K_n and G_(0,n), Proc. Int. Conf. on App. Math. and Theoretical Comp. Sci.,

St. Xavier’s College of Engg., Nagercoil, TN, India (2013), pp. 296 – 303.

V. Vilfred, R. Kala and A. Suryakala, Number of Triangles in Integral Sum Graphs Gm,n, IJ of Algorithms, Computing and Mathematics, 4 (2011), pp. 16-24.

V. Vilfred and L. Mary Florida, Anti-integral sum graphs and decomposition of G_n, G_n^c and K_n, Proc. Int. Conf. on App. Math. and Theoretical Comp. Sci., St. Xavier’s College of Engg., Nagercoil, TN, India (2013), pp. 129-133.

V. Vilfred and L. Mary Florida, Integral sum graphs and maximal integral sum graphs, Graph Theory Notes of New York, MAA, 63 (2012), pp. 28-36.

V. Vilfred and L. Mary Florida, Integral sum graphs H_( X,Y)^(R,T), edge sum class and edge sum color number, Proc. Int. Conf. on Math. in Engg. and Business Management, Stella Maris College, Chennai, India (2012), pp. 88 - 94.

V. Vilfred and L. Mary Florida, New families of integral sum graphs - edge sum class and chromatic integral sum number, Proc. Int. Conf. on App. Math. and Theoretical Comp. Sci., St. Xavier’s Catholic College of Engg., Nagercoil, TN, India (2013), pp. 177 - 182.

V. Vilfred and L. Mary Florida, Sum number and exclusiveness of graphs C4, Ln and P3 □ P3, Proc. Inter. Conf. on Math. in Engg. and Business Management, Stella Maris College, Chennai, India (2012), pp. 13 - 15.

V. Vilfred and T. Nicholas, Amalgamation of integral sum graphs, fan and Dutch M-Windmill are integral sum graphs, Graph Theory Notes of New York, MAA, 58 (2010), pp. 51-54.

V. Vilfred and T. Nicholas, Banana trees and union of stars are integral sum graphs, Ars Comb., 102 (2011), pp. 79-85.

V. Vilfred and T. Nicholas, The integral sum graph G_n, Graph Theory Notes of New York, MAA, 57 (2009), pp. 43-47.

V. Vilfred and K. Rubin Mary, Number of Cycles of Length Four in the Integral Sum Graphs Gm,n, Proc. Inter. Conf. on App. Math. and Theoretical Comp. Sci.,

St. Xavier’s College of Engg., Nagercoil, TN, India (2013), pp. 134 – 141.

V. Vilfred and A. Suryakala, More properties of sum graphs, Proc. Int. Conf. on App. Math. and Theoretical Comp. Sci., St. Xavier’s College of Engg., Nagercoil, TN, India (2013), pp. 142-145.

V. Vilfred, A. Suryakala and K. Rubin Mary, More on integral sum graphs, Proc. Int. Conf. on App. Math. and Theoretical Comp. Sci., St. Xavier’s College of Engg., Nagercoil, TN, India (2013), pp. 173 – 176.

DOI: https://doi.org/10.22342/jims.20.2.172.148-159

### Refbacks

- There are currently no refbacks.

**Journal of the Indonesian Mathematical Society** ( p-ISSN:2086-8952 | e-ISSN:2460-0245) published by the Indonesian Mathematical Society (IndoMS).

**Indexed by**:

**Visitor Number** : View My Stats

Journal of the Indonesian Mathematical Society by http://jims-a.org/index.php/jimsa is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.