Vertex Equitable Labeling of Cyclic Snakes and Bistar Graphs - Jeyanthi, P.; Maheswari, A. (Journal of Scientific Research, 2013)
<!–[if !mso]> <mce:style><! v\:* behavior:url(#default#VML); o\:* behavior:url(#default#VML); w\:* behavior:url(#default#VML); .shape behavior:url(#default#VML); –> <!–[endif] –> <!–[if gte mso 9]> <![endif]–><!–[if gte mso 9]> Normal 0 false false false EN-US X-NONE X-NONE <![endif]–><!–[if gte mso 9]> <![endif]–><!–[if gte mso 10]> <mce:style><! /* Style Definitions */ table.MsoNormalTable mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; –> <!–[endif] –> Let G be a graph with p vertices and q edges and let A = 0, 1, 2,..., . A vertex labeling f: V (G) ® A induces an edge labeling f * defined by f *(uv) = f(u) + f(v) for all edges uv. For , let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, and the induced edge labels are 1, 2, 3, , q. In this paper, we establish vertex equitable labeling of square graph of and splitting graph of and kC4 snake(k?1) and the generalized kCn snake is vertex equitable if nº0(mod4),n?4. Keywords: Vertex equitable labeling; Vertex equitable graph. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i1.15044 J. Sci. Res. 6 (1), 79-85 (2014)