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On Lict sigraphs | ||
| Transactions on Combinatorics | ||
| مقاله 17، دوره 3، شماره 4، اسفند 2014، صفحه 11-18 اصل مقاله (321.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.5627 | ||
| نویسندگان | ||
| Veena Mathad* 1؛ Kishori P. Narayankar2 | ||
| 1University of Mysore | ||
| 2Mangalore University | ||
| چکیده | ||
| A signed graph (marked graph) is an ordered pair $S=(G,\sigma)$ $(S=(G,\mu))$, where $G=(V,E)$ is a graph called the underlying graph of $S$ and $\sigma:E\rightarrow\{+,-\}$ $(\mu:V\rightarrow\{+,-\})$ is a function. For a graph $G$, $V(G), E(G)$ and $C(G)$ denote its vertex set, edge set and cut-vertex set, respectively. The lict graph $L_{c}(G)$ of a graph $G=(V,E)$ is defined as the graph having vertex set $E(G)\cup C(G)$ in which two vertices are adjacent if and only if they correspond to adjacent edges of $G$ or one corresponds to an edge $e_{i}$ of $G$ and the other corresponds to a cut-vertex $c_{j}$ of $G$ such that $e_{i}$ is incident with $c_{j}$. In this paper, we introduce lict sigraphs, as a natural extension of the notion of lict graph to the realm of signed graphs. We show that every lict sigraph is balanced. We characterize signed graphs $S$ and $S^{'}$ for which $S\sim L_{c}(S)$, $\eta(S)\sim L_{c}(S)$, $L(S)\sim L_{c}(S')$, $J(S)\sim L_{c}(S^{'})$ and $T_{1}(S)\sim L_{c}(S^{'})$, where $\eta(S)$, $L(S)$, $J(S)$ and $T_{1}(S)$ are negation, line graph, jump graph and semitotal line sigraph of $S$, respectively, and $\sim$ means switching equivalence. | ||
| کلیدواژهها | ||
| signed graph؛ Line sigraph؛ Jump sigraph؛ Semitotal line sigraph؛ Lict sigraph | ||
| مراجع | ||
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R. P. Abelson and M. J. Rosenberg (1958) Symbolic Psychologic: A model of attitudinal cognition Behav. Sci. 3, 1-13
M. Acharya (2009) $\times$-line Signed Graphs J. Combin. Math. Combin. Comput. 69, 103-111
M. Acharya and D. Sinha (2003) A characterization of signed graphs that are switching equivalent to their jump sigraphs Graph Theory Notes of New York XLIV, 30-34
L. W. Beineke and F. Harary (1978) Consistency in marked graphs J. Math. Psychol. 18 (3), 260-269
B. Basavanagoud and Veena N. Mathad (2005) Graph equations for line graphs, jump graphs,
middle graphs, litact graphs and lict graphs Acta Cienc. Indica Math. 31 (3), 735-740
G. Chartrand, H. Hevia, E. B. Jarrett and M. Schultz (1997) Subgraph distance in graphs defined by edge transfers Discrete Math. 170, 63-79
D. Sinha and P. Garg (2011) Characterization of Total Signed Graph and Semi-total Signed Graphs Int. J. Contemp. Math. Sci. 6 (5), 221-228
F. Harary (1969) Graph Theory Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London
F. Harary (1953-54) On the notion of balance of a signed graph Michigan Math. J. 2, 143-146
F. Harary (1957) Structural duality Behavioral Sci. 2 (4), 255-265
V. R. Kulli and M. H. Muddebihal (2006) The Lict graph and litact graph of a graph J. of Analysis and Comput. 2 (1), 33-43
E. Sampathkumar (1984) Point signed and line signed graphs Nat. Acad. Sci. Lett. 7 (3), 91-93
E. Sampathkumar and S. B. Chikkodimath (1973) Semitotal graphs of a graph-II J. Karnatak Univ. Sci. 18, 281-284
T. Sozansky (1980) Enumeration of weak isomorphism classes of signed graphs J. Graph Theory 4 (2), 127-144
T. Zaslavski (1998) A mathematical bibliography of signed and gain graphs and its allied areas Electronic J. Combin. 8 (1)
T. Zaslavski (1982) Signed graphs Discrete Appl. Math. 4 (1), 47-74
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